Finite Group Databasebeta

← Group #72236946

Character table — Group #72236946

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size1111222222444444444488888888888888888888816161616161632323232323211112222224444444444888888888888888888888161616161616323232323232
order1222222222222222222222244444444444444444424444444448822222222222222222222222444444444444444444244444444488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111
χ51111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1
χ61111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111
χ71111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111
χ81111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1
χ911111-1-11-1-11111-1-1-1-1111-1-11iiii−i−i−i−iiiii−i−i−i−i-11-1-111-11-1i−ii−i11111-1-11-1-11111-1-1-1-1111-1-11iiii−i−i−i−iiiii−i−i−i−i-11-1-111-11-1i−ii−i
χ1011111-1-11-1-11111-1-1-1-1111-1-11iiii−i−i−i−iiiii−i−i−i−i-1-111-11-1-11−ii−ii11111-1-11-1-11111-1-1-1-1111-1-11iiii−i−i−i−iiiii−i−i−i−i-1-111-11-1-11−ii−ii
χ1111111-1-11-1-11111-1-1-1-1111-1-11−i−i−i−iiiii−i−i−i−iiiii-11-1-111-11-1−ii−ii11111-1-11-1-11111-1-1-1-1111-1-11−i−i−i−iiiii−i−i−i−iiiii-11-1-111-11-1−ii−ii
χ1211111-1-11-1-11111-1-1-1-1111-1-11−i−i−i−iiiii−i−i−i−iiiii-1-111-11-1-11i−ii−i11111-1-11-1-11111-1-1-1-1111-1-11−i−i−i−iiiii−i−i−i−iiiii-1-111-11-1-11i−ii−i
χ1311111-1-11-1-1-1-1-1-11111111-1-11iiii−i−i−i−i−i−i−i−iiiii-11-1-11-11-11i−i−ii11111-1-11-1-1-1-1-1-11111111-1-11iiii−i−i−i−i−i−i−i−iiiii-11-1-11-11-11i−i−ii
χ1411111-1-11-1-1-1-1-1-11111111-1-11iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111-1−iii−i11111-1-11-1-1-1-1-1-11111111-1-11iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111-1−iii−i
χ1511111-1-11-1-1-1-1-1-11111111-1-11−i−i−i−iiiiiiiii−i−i−i−i-11-1-11-11-11−iii−i11111-1-11-1-1-1-1-1-11111111-1-11−i−i−i−iiiiiiiii−i−i−i−i-11-1-11-11-11−iii−i
χ1611111-1-11-1-1-1-1-1-11111111-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111-1i−i−ii11111-1-11-1-1-1-1-1-11111111-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111-1i−i−ii
χ17222222222200000000-2-22-22-222-2-222-2-200000000-2000000000000222222222200000000-2-22-22-222-2-222-2-200000000-2000000000000
χ18222222222200000000-2-22-22-2-2-222-2-22200000000-2000000000000222222222200000000-2-22-22-2-2-222-2-22200000000-2000000000000
χ19222222222200000000-2-2-2-2-220000000022-2-222-2-22000000000000222222222200000000-2-2-2-2-220000000022-2-222-2-22000000000000
χ20222222222200000000-2-2-2-2-2200000000-2-222-2-2222000000000000222222222200000000-2-2-2-2-2200000000-2-222-2-2222000000000000
χ2122222222222222222222-22-2-20000000000000000-20000-2-200000022222222222222222222-22-2-20000000000000000-20000-2-2000000
χ222222222222-2-2-2-2-2-2-2-222-22-2-20000000000000000-20000220000002222222222-2-2-2-2-2-2-2-222-22-2-20000000000000000-2000022000000
χ2322222-2-22-2-200000000-2-222-2-22i2i−2i−2i−2i−2i2i2i00000000200000000000022222-2-22-2-200000000-2-222-2-22i2i−2i−2i−2i−2i2i2i000000002000000000000
χ2422222-2-22-2-200000000-2-222-2-2−2i−2i2i2i2i2i−2i−2i00000000200000000000022222-2-22-2-200000000-2-222-2-2−2i−2i2i2i2i2i−2i−2i000000002000000000000
χ2522222-2-22-2-200000000-2-2-2222000000002i2i−2i−2i−2i−2i2i2i-200000000000022222-2-22-2-200000000-2-2-2222000000002i2i−2i−2i−2i−2i2i2i-2000000000000
χ2622222-2-22-2-200000000-2-2-222200000000−2i−2i2i2i2i2i−2i−2i-200000000000022222-2-22-2-200000000-2-2-222200000000−2i−2i2i2i2i2i−2i−2i-2000000000000
χ2722222-2-22-2-22222-2-2-2-222-2-22-2000000000000000020000-2200000022222-2-22-2-22222-2-2-2-222-2-22-2000000000000000020000-22000000
χ2822222-2-22-2-2-2-2-2-2222222-2-22-20000000000000000200002-200000022222-2-22-2-2-2-2-2-2222222-2-22-20000000000000000200002-2000000
χ294444-44-4-44-4000000000000000000000000000000022-2-2000000004444-44-4-44-4000000000000000000000000000000022-2-200000000
χ304444-44-4-44-40000000000000000000000000000000-2-222000000004444-44-4-44-40000000000000000000000000000000-2-22200000000
χ314444-4-44-4-4400000000000000000000000000000002-22-2000000004444-4-44-4-4400000000000000000000000000000002-22-200000000
χ324444-4-44-4-440000000000000000000000000000000-22-22000000004444-4-44-4-440000000000000000000000000000000-22-2200000000
χ3344-4-400400-422-2-222-2-2000000002i−2i002i−2i2i−2i002i−2i00000000000000044-4-400400-422-2-222-2-2000000002i−2i002i−2i2i−2i002i−2i000000000000000
χ3444-4-400400-422-2-222-2-200000000−2i2i00−2i2i−2i2i00−2i2i00000000000000044-4-400400-422-2-222-2-200000000−2i2i00−2i2i−2i2i00−2i2i000000000000000
χ3544-4-400400-4-2-222-2-222000000002i−2i002i−2i−2i2i00−2i2i00000000000000044-4-400400-4-2-222-2-222000000002i−2i002i−2i−2i2i00−2i2i000000000000000
χ3644-4-400400-4-2-222-2-22200000000−2i2i00−2i2i2i−2i002i−2i00000000000000044-4-400400-4-2-222-2-22200000000−2i2i00−2i2i2i−2i002i−2i000000000000000
χ3744-4-400-400422-2-2-2-222000000002-200-222-200-2200000000000000044-4-400-400422-2-2-2-222000000002-200-222-200-22000000000000000
χ3844-4-400-400422-2-2-2-22200000000-22002-2-22002-200000000000000044-4-400-400422-2-2-2-22200000000-22002-2-22002-2000000000000000
χ3944-4-400-4004-2-22222-2-2000000002-200-22-22002-200000000000000044-4-400-4004-2-22222-2-2000000002-200-22-22002-2000000000000000
χ4044-4-400-4004-2-22222-2-200000000-22002-22-200-2200000000000000044-4-400-4004-2-22222-2-200000000-22002-22-200-22000000000000000
χ414-44-40400-402-22-22-22-20000002i−2i002i−2i00002i−2i002i−2i00000000000004-44-40400-402-22-22-22-20000002i−2i002i−2i00002i−2i002i−2i0000000000000
χ424-44-40400-402-22-22-22-2000000−2i2i00−2i2i0000−2i2i00−2i2i00000000000004-44-40400-402-22-22-22-2000000−2i2i00−2i2i0000−2i2i00−2i2i0000000000000
χ434-44-40400-40-22-22-22-220000002i−2i002i−2i0000−2i2i00−2i2i00000000000004-44-40400-40-22-22-22-220000002i−2i002i−2i0000−2i2i00−2i2i0000000000000
χ444-44-40400-40-22-22-22-22000000−2i2i00−2i2i00002i−2i002i−2i00000000000004-44-40400-40-22-22-22-22000000−2i2i00−2i2i00002i−2i002i−2i0000000000000
χ454-44-40-400402-22-2-22-220000002-200-2200002-200-2200000000000004-44-40-400402-22-2-22-220000002-200-2200002-200-220000000000000
χ464-44-40-400402-22-2-22-22000000-22002-20000-22002-200000000000004-44-40-400402-22-2-22-22000000-22002-20000-22002-20000000000000
χ474-44-40-40040-22-222-22-20000002-200-220000-22002-200000000000004-44-40-40040-22-222-22-20000002-200-220000-22002-20000000000000
χ484-44-40-40040-22-222-22-2000000-22002-200002-200-2200000000000004-44-40-40040-22-222-22-2000000-22002-200002-200-220000000000000
χ494-4-44-40040000004-4-444-40000000000000000000000000000000004-4-44-40040000004-4-444-4000000000000000000000000000000000
χ504-4-44-4004000000-444-44-40000000000000000000000000000000004-4-44-4004000000-444-44-4000000000000000000000000000000000
χ514-4-44-4004004-4-440000-440000000000000000000000000000000004-4-44-4004004-4-440000-44000000000000000000000000000000000
χ524-4-44-400400-444-40000-440000000000000000000000000000000004-4-44-400400-444-40000-44000000000000000000000000000000000
χ538-8-88800-80000000000000000000000000000000000000000000008-8-88800-8000000000000000000000000000000000000000000000
χ5411111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5511111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ56111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11111
χ57111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11111-1-111-1-1-1-1
χ581111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-111
χ591111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-1-111-1-1
χ601111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ6211111-1-11-1-11111-1-1-1-1111-1-11iiii−i−i−i−iiiii−i−i−i−i-11-1-111-11-1i−ii−i-1-1-1-1-111-111-1-1-1-11111-1-1-111-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-11−ii−ii
χ6311111-1-11-1-11111-1-1-1-1111-1-11iiii−i−i−i−iiiii−i−i−i−i-1-111-11-1-11−ii−ii-1-1-1-1-111-111-1-1-1-11111-1-1-111-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1i−ii−i
χ6411111-1-11-1-11111-1-1-1-1111-1-11−i−i−i−iiiii−i−i−i−iiiii-11-1-111-11-1−ii−ii-1-1-1-1-111-111-1-1-1-11111-1-1-111-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-11-11i−ii−i
χ6511111-1-11-1-11111-1-1-1-1111-1-11−i−i−i−iiiii−i−i−i−iiiii-1-111-11-1-11i−ii−i-1-1-1-1-111-111-1-1-1-11111-1-1-111-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1−ii−ii
χ6611111-1-11-1-1-1-1-1-11111111-1-11iiii−i−i−i−i−i−i−i−iiiii-11-1-11-11-11i−i−ii-1-1-1-1-111-1111111-1-1-1-1-1-1-111-1−i−i−i−iiiiiiiii−i−i−i−i1-111-11-11-1−iii−i
χ6711111-1-11-1-1-1-1-1-11111111-1-11iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111-1−iii−i-1-1-1-1-111-1111111-1-1-1-1-1-1-111-1−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-11i−i−ii
χ6811111-1-11-1-1-1-1-1-11111111-1-11−i−i−i−iiiiiiiii−i−i−i−i-11-1-11-11-11−iii−i-1-1-1-1-111-1111111-1-1-1-1-1-1-111-1iiii−i−i−i−i−i−i−i−iiiii1-111-11-11-1i−i−ii
χ6911111-1-11-1-1-1-1-1-11111111-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111-1i−i−ii-1-1-1-1-111-1111111-1-1-1-1-1-1-111-1iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-11−iii−i
χ70222222222200000000-2-22-22-222-2-222-2-200000000-2000000000000-2-2-2-2-2-2-2-2-2-20000000022-22-22-2-222-2-222000000002000000000000
χ71222222222200000000-2-22-22-2-2-222-2-22200000000-2000000000000-2-2-2-2-2-2-2-2-2-20000000022-22-2222-2-222-2-2000000002000000000000
χ72222222222200000000-2-2-2-2-220000000022-2-222-2-22000000000000-2-2-2-2-2-2-2-2-2-20000000022222-200000000-2-222-2-222-2000000000000
χ73222222222200000000-2-2-2-2-2200000000-2-222-2-2222000000000000-2-2-2-2-2-2-2-2-2-20000000022222-20000000022-2-222-2-2-2000000000000
χ7422222222222222222222-22-2-20000000000000000-20000-2-2000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-22200000000000000002000022000000
χ752222222222-2-2-2-2-2-2-2-222-22-2-20000000000000000-2000022000000-2-2-2-2-2-2-2-2-2-222222222-2-22-222000000000000000020000-2-2000000
χ7622222-2-22-2-200000000-2-222-2-22i2i−2i−2i−2i−2i2i2i000000002000000000000-2-2-2-2-222-2220000000022-2-222−2i−2i2i2i2i2i−2i−2i00000000-2000000000000
χ7722222-2-22-2-200000000-2-222-2-2−2i−2i2i2i2i2i−2i−2i000000002000000000000-2-2-2-2-222-2220000000022-2-2222i2i−2i−2i−2i−2i2i2i00000000-2000000000000
χ7822222-2-22-2-200000000-2-2-2222000000002i2i−2i−2i−2i−2i2i2i-2000000000000-2-2-2-2-222-22200000000222-2-2-200000000−2i−2i2i2i2i2i−2i−2i2000000000000
χ7922222-2-22-2-200000000-2-2-222200000000−2i−2i2i2i2i2i−2i−2i-2000000000000-2-2-2-2-222-22200000000222-2-2-2000000002i2i−2i−2i−2i−2i2i2i2000000000000
χ8022222-2-22-2-22222-2-2-2-222-2-22-2000000000000000020000-22000000-2-2-2-2-222-222-2-2-2-22222-2-222-220000000000000000-200002-2000000
χ8122222-2-22-2-2-2-2-2-2222222-2-22-20000000000000000200002-2000000-2-2-2-2-222-2222222-2-2-2-2-2-222-220000000000000000-20000-22000000
χ824444-44-4-44-4000000000000000000000000000000022-2-200000000-4-4-4-44-444-440000000000000000000000000000000-2-22200000000
χ834444-44-4-44-40000000000000000000000000000000-2-22200000000-4-4-4-44-444-44000000000000000000000000000000022-2-200000000
χ844444-4-44-4-4400000000000000000000000000000002-22-200000000-4-4-4-444-444-40000000000000000000000000000000-22-2200000000
χ854444-4-44-4-440000000000000000000000000000000-22-2200000000-4-4-4-444-444-400000000000000000000000000000002-22-200000000
χ8644-4-400400-422-2-222-2-2000000002i−2i002i−2i2i−2i002i−2i000000000000000-4-44400-4004-2-222-2-22200000000−2i2i00−2i2i−2i2i00−2i2i000000000000000
χ8744-4-400400-422-2-222-2-200000000−2i2i00−2i2i−2i2i00−2i2i000000000000000-4-44400-4004-2-222-2-222000000002i−2i002i−2i2i−2i002i−2i000000000000000
χ8844-4-400400-4-2-222-2-222000000002i−2i002i−2i−2i2i00−2i2i000000000000000-4-44400-400422-2-222-2-200000000−2i2i00−2i2i2i−2i002i−2i000000000000000
χ8944-4-400400-4-2-222-2-22200000000−2i2i00−2i2i2i−2i002i−2i000000000000000-4-44400-400422-2-222-2-2000000002i−2i002i−2i−2i2i00−2i2i000000000000000
χ9044-4-400-400422-2-2-2-222000000002-200-222-200-22000000000000000-4-44400400-4-2-22222-2-200000000-22002-2-22002-2000000000000000
χ9144-4-400-400422-2-2-2-22200000000-22002-2-22002-2000000000000000-4-44400400-4-2-22222-2-2000000002-200-222-200-22000000000000000
χ9244-4-400-4004-2-22222-2-2000000002-200-22-22002-2000000000000000-4-44400400-422-2-2-2-22200000000-22002-22-200-22000000000000000
χ9344-4-400-4004-2-22222-2-200000000-22002-22-200-22000000000000000-4-44400400-422-2-2-2-222000000002-200-22-22002-2000000000000000
χ944-44-40400-402-22-22-22-20000002i−2i002i−2i00002i−2i002i−2i0000000000000-44-440-40040-22-22-22-22000000−2i2i00−2i2i0000−2i2i00−2i2i0000000000000
χ954-44-40400-402-22-22-22-2000000−2i2i00−2i2i0000−2i2i00−2i2i0000000000000-44-440-40040-22-22-22-220000002i−2i002i−2i00002i−2i002i−2i0000000000000
χ964-44-40400-40-22-22-22-220000002i−2i002i−2i0000−2i2i00−2i2i0000000000000-44-440-400402-22-22-22-2000000−2i2i00−2i2i00002i−2i002i−2i0000000000000
χ974-44-40400-40-22-22-22-22000000−2i2i00−2i2i00002i−2i002i−2i0000000000000-44-440-400402-22-22-22-20000002i−2i002i−2i0000−2i2i00−2i2i0000000000000
χ984-44-40-400402-22-2-22-220000002-200-2200002-200-220000000000000-44-440400-40-22-222-22-2000000-22002-20000-22002-20000000000000
χ994-44-40-400402-22-2-22-22000000-22002-20000-22002-20000000000000-44-440400-40-22-222-22-20000002-200-2200002-200-220000000000000
χ1004-44-40-40040-22-222-22-20000002-200-220000-22002-20000000000000-44-440400-402-22-2-22-22000000-22002-200002-200-220000000000000
χ1014-44-40-40040-22-222-22-2000000-22002-200002-200-220000000000000-44-440400-402-22-2-22-220000002-200-220000-22002-20000000000000
χ1024-4-44-40040000004-4-444-4000000000000000000000000000000000-444-4400-4000000-444-4-44000000000000000000000000000000000
χ1034-4-44-4004000000-444-44-4000000000000000000000000000000000-444-4400-40000004-4-44-44000000000000000000000000000000000
χ1044-4-44-4004004-4-440000-44000000000000000000000000000000000-444-4400-400-444-400004-4000000000000000000000000000000000
χ1054-4-44-400400-444-40000-44000000000000000000000000000000000-444-4400-4004-4-4400004-4000000000000000000000000000000000
χ1068-8-88800-8000000000000000000000000000000000000000000000-888-8-8008000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).