Finite Group Databasebeta

← Group #72283859

Character table — Group #72283859

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size111122444444444488888888888888888816161616161616161616161632323232111122444444444488888888888888888816161616161616161616161632323232
order1222222222224444222222444444444444444444444444888822222222222244442222224444444444444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-11111111111111-1-1-1-11-1-11111-1-1-1-1111111111111111111-1-1-1-11111111111111-1-1-1-11-1-11111-1-1-1-1
χ4111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-11111
χ51111111111111111-1-111-1-111-1-111111111-11-11-1-11-1-1-1-1-111-1-11111111111111111-1-111-1-111-1-111111111-11-11-1-11-1-1-1-1-111-1-1
χ61111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-11-11111-1-1111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-11-11111-1-111
χ71111111111111111-1-1-1-11111-1-111111111-1-11-11-1-11-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-111111111-1-11-11-1-11-1-1-1-1-1-111
χ81111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111111-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1111-1-1ii−i−ii−ii−i11111111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1111-1-1ii−i−ii−ii−i
χ1011111111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1111-1-1−i−iii−ii−ii11111111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1111-1-1−i−iii−ii−ii
χ1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−i-111-1-1111ii−i−i−ii−ii11111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−i-111-1-1111ii−i−i−ii−ii
χ1211111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii-111-1-1111−i−iiii−ii−i11111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii-111-1-1111−i−iiii−ii−i
χ1311111111-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i1-111-1-1-11−i−iiii−i−ii11111111-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i1-111-1-1-11−i−iiii−i−ii
χ1411111111-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiii1-111-1-1-11ii−i−i−iii−i11111111-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiii1-111-1-1-11ii−i−i−iii−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i11-1-11-11-1−i−iii−iii−i11111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i11-1-11-11-1−i−iii−iii−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii11-1-11-11-1ii−i−ii−i−ii11111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii11-1-11-11-1ii−i−ii−i−ii
χ17222222222222-2-2-2-2220000-2-2-2-20000000020000-20000000000222222222222-2-2-2-2220000-2-2-2-20000000020000-20000000000
χ18222222222222-2-2-2-2-2-20000-2-22200000000-2000020000000000222222222222-2-2-2-2-2-20000-2-22200000000-2000020000000000
χ1922222222-2-2-2-22222220000-2-22200000000-20000-2000000000022222222-2-2-2-22222220000-2-22200000000-20000-20000000000
χ2022222222-2-2-2-22222-2-20000-2-2-2-200000000200002000000000022222222-2-2-2-22222-2-20000-2-2-2-2000000002000020000000000
χ21222222-2-22-22-222-2-20000222-200000000000020-200-200000000222222-2-22-22-222-2-20000222-200000000000020-200-200000000
χ22222222-2-22-22-222-2-20000-2-22-2000000000000-20200200000000222222-2-22-22-222-2-20000-2-22-2000000000000-20200200000000
χ23222222-2-22-22-2-2-222002200-220000000000020-200-2000000000222222-2-22-22-2-2-222002200-220000000000020-200-2000000000
χ24222222-2-22-22-2-2-22200-2-200-2200000000000-202002000000000222222-2-22-22-2-2-22200-2-200-2200000000000-202002000000000
χ25222222-2-2-22-2222-2-2002200-2200000000000-20-2002000000000222222-2-2-22-2222-2-2002200-2200000000000-20-2002000000000
χ26222222-2-2-22-2222-2-200-2-200-220000000000020200-2000000000222222-2-2-22-2222-2-200-2-200-220000000000020200-2000000000
χ27222222-2-2-22-22-2-2220000222-2000000000000-20-200200000000222222-2-2-22-22-2-2220000222-2000000000000-20-200200000000
χ28222222-2-2-22-22-2-2220000-2-22-200000000000020200-200000000222222-2-2-22-22-2-2220000-2-22-200000000000020200-200000000
χ2922-2-22-22-200002i−2i2i−2i2-20000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001+i−1−i1−i−1+i000022-2-22-22-200002i−2i2i−2i2-20000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001+i−1−i1−i−1+i0000
χ3022-2-22-22-200002i−2i2i−2i2-20000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1−i1+i−1+i1−i000022-2-22-22-200002i−2i2i−2i2-20000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1−i1+i−1+i1−i0000
χ3122-2-22-22-200002i−2i2i−2i-22000000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1−i1+i−1+i1−i000022-2-22-22-200002i−2i2i−2i-22000000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1−i1+i−1+i1−i0000
χ3222-2-22-22-200002i−2i2i−2i-22000000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001+i−1−i1−i−1+i000022-2-22-22-200002i−2i2i−2i-22000000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001+i−1−i1−i−1+i0000
χ3322-2-22-22-20000−2i2i−2i2i2-2000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i−1+i1+i−1−i000022-2-22-22-20000−2i2i−2i2i2-2000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i−1+i1+i−1−i0000
χ3422-2-22-22-20000−2i2i−2i2i2-2000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i1−i−1−i1+i000022-2-22-22-20000−2i2i−2i2i2-2000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i1−i−1−i1+i0000
χ3522-2-22-22-20000−2i2i−2i2i-220000002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1+i1−i−1−i1+i000022-2-22-22-20000−2i2i−2i2i-220000002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1+i1−i−1−i1+i0000
χ3622-2-22-22-20000−2i2i−2i2i-220000002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001−i−1+i1+i−1−i000022-2-22-22-20000−2i2i−2i2i-220000002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001−i−1+i1+i−1−i0000
χ374444-4-40040-40000000000000002i−2i2i−2i2i−2i2i−2i00000000000000004444-4-40040-40000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ384444-4-40040-4000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000004444-4-40040-4000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ394444-4-400-4040000000000000002-22-2-22-2200000000000000004444-4-400-4040000000000000002-22-2-22-220000000000000000
χ404444-4-400-404000000000000000-22-222-22-200000000000000004444-4-400-404000000000000000-22-222-22-20000000000000000
χ4144-4-44-4-4400004i−4i−4i4i000000000000000000000000000000000044-4-44-4-4400004i−4i−4i4i0000000000000000000000000000000000
χ4244-4-44-4-440000−4i4i4i−4i000000000000000000000000000000000044-4-44-4-440000−4i4i4i−4i0000000000000000000000000000000000
χ4344-4-4-4400040-4000000000000002i−2i−2i2i2i−2i−2i2i000000000000000044-4-4-4400040-4000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ4444-4-4-4400040-400000000000000−2i2i2i−2i−2i2i2i−2i000000000000000044-4-4-4400040-400000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ4544-4-4-44000-404000000000000002-2-22-222-2000000000000000044-4-4-44000-404000000000000002-2-22-222-20000000000000000
χ4644-4-4-44000-40400000000000000-222-22-2-22000000000000000044-4-4-44000-40400000000000000-222-22-2-220000000000000000
χ478-88-800000000000000004-400000000000000000000000000008-88-800000000000000004-40000000000000000000000000000
χ488-88-80000000000000000-4400000000000000000000000000008-88-80000000000000000-440000000000000000000000000000
χ498-8-88000000000000004-40000000000000000000000000000008-8-88000000000000004-4000000000000000000000000000000
χ508-8-8800000000000000-440000000000000000000000000000008-8-8800000000000000-44000000000000000000000000000000
χ5111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5211111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ53111111111111111111-1-1-1-11111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11111
χ54111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11111-1111111-1-1-1-1
χ551111111111111111-1-111-1-111-1-111111111-11-11-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11-11-111-111111-1-111
χ561111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-11-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111111-11-111-11-1-1-1-111-1-1
χ571111111111111111-1-1-1-11111-1-111111111-1-11-11-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-11-111-1111111-1-1
χ581111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-11-111-1-1-1-1-1-1-111
χ5911111111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1111-1-1ii−i−ii−ii−i-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii111-1-1-111−i−iii−ii−ii
χ6011111111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1111-1-1−i−iii−ii−ii-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111iiii−i−i−i−i111-1-1-111ii−i−ii−ii−i
χ6111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−i-111-1-1111ii−i−i−ii−ii-1-1-1-1-1-1-1-111111111-1-11111-1-111−i−i−i−iiiii1-1-111-1-1-1−i−iiii−ii−i
χ6211111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii-111-1-1111−i−iiii−ii−i-1-1-1-1-1-1-1-111111111-1-11111-1-111iiii−i−i−i−i1-1-111-1-1-1ii−i−i−ii−ii
χ6311111111-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i1-111-1-1-11−i−iiii−i−ii-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1−i−i−i−iiiii-11-1-1111-1ii−i−i−iii−i
χ6411111111-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiii1-111-1-1-11ii−i−i−iii−i-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1iiii−i−i−i−i-11-1-1111-1−i−iiii−i−ii
χ6511111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i11-1-11-11-1−i−iii−iii−i-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-111-11-11ii−i−ii−i−ii
χ6611111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii11-1-11-11-1ii−i−ii−i−ii-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-111-11-11−i−iii−iii−i
χ67222222222222-2-2-2-2220000-2-2-2-20000000020000-20000000000-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000222200000000-2000020000000000
χ68222222222222-2-2-2-2-2-20000-2-22200000000-2000020000000000-2-2-2-2-2-2-2-2-2-2-2-2222222000022-2-20000000020000-20000000000
χ6922222222-2-2-2-22222220000-2-22200000000-20000-20000000000-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000022-2-2000000002000020000000000
χ7022222222-2-2-2-22222-2-20000-2-2-2-2000000002000020000000000-2-2-2-2-2-2-2-22222-2-2-2-2220000222200000000-20000-20000000000
χ71222222-2-22-22-222-2-20000222-200000000000020-200-200000000-2-2-2-2-2-222-22-22-2-2220000-2-2-22000000000000-20200200000000
χ72222222-2-22-22-222-2-20000-2-22-2000000000000-20200200000000-2-2-2-2-2-222-22-22-2-222000022-2200000000000020-200-200000000
χ73222222-2-22-22-2-2-222002200-220000000000020-200-2000000000-2-2-2-2-2-222-22-2222-2-200-2-2002-200000000000-202002000000000
χ74222222-2-22-22-2-2-22200-2-200-2200000000000-202002000000000-2-2-2-2-2-222-22-2222-2-20022002-20000000000020-200-2000000000
χ75222222-2-2-22-2222-2-2002200-2200000000000-20-2002000000000-2-2-2-2-2-2222-22-2-2-22200-2-2002-20000000000020200-2000000000
χ76222222-2-2-22-2222-2-200-2-200-220000000000020200-2000000000-2-2-2-2-2-2222-22-2-2-2220022002-200000000000-20-2002000000000
χ77222222-2-2-22-22-2-2220000222-2000000000000-20-200200000000-2-2-2-2-2-2222-22-222-2-20000-2-2-2200000000000020200-200000000
χ78222222-2-2-22-22-2-2220000-2-22-200000000000020200-200000000-2-2-2-2-2-2222-22-222-2-2000022-22000000000000-20-200200000000
χ7922-2-22-22-200002i−2i2i−2i2-20000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001+i−1−i1−i−1+i0000-2-222-22-220000−2i2i−2i2i-22000000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1−i1+i−1+i1−i0000
χ8022-2-22-22-200002i−2i2i−2i2-20000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1−i1+i−1+i1−i0000-2-222-22-220000−2i2i−2i2i-22000000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001+i−1−i1−i−1+i0000
χ8122-2-22-22-200002i−2i2i−2i-22000000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1−i1+i−1+i1−i0000-2-222-22-220000−2i2i−2i2i2-20000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001+i−1−i1−i−1+i0000
χ8222-2-22-22-200002i−2i2i−2i-22000000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001+i−1−i1−i−1+i0000-2-222-22-220000−2i2i−2i2i2-20000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1−i1+i−1+i1−i0000
χ8322-2-22-22-20000−2i2i−2i2i2-2000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i−1+i1+i−1−i0000-2-222-22-2200002i−2i2i−2i-220000002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i1−i−1−i1+i0000
χ8422-2-22-22-20000−2i2i−2i2i2-2000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i1−i−1−i1+i0000-2-222-22-2200002i−2i2i−2i-220000002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i−1+i1+i−1−i0000
χ8522-2-22-22-20000−2i2i−2i2i-220000002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1+i1−i−1−i1+i0000-2-222-22-2200002i−2i2i−2i2-2000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001−i−1+i1+i−1−i0000
χ8622-2-22-22-20000−2i2i−2i2i-220000002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001−i−1+i1+i−1−i0000-2-222-22-2200002i−2i2i−2i2-2000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1+i1−i−1−i1+i0000
χ874444-4-40040-40000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000-4-4-4-44400-404000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ884444-4-40040-4000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000-4-4-4-44400-4040000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ894444-4-400-4040000000000000002-22-2-22-220000000000000000-4-4-4-4440040-4000000000000000-22-222-22-20000000000000000
χ904444-4-400-404000000000000000-22-222-22-20000000000000000-4-4-4-4440040-40000000000000002-22-2-22-220000000000000000
χ9144-4-44-4-4400004i−4i−4i4i0000000000000000000000000000000000-4-444-444-40000−4i4i4i−4i0000000000000000000000000000000000
χ9244-4-44-4-440000−4i4i4i−4i0000000000000000000000000000000000-4-444-444-400004i−4i−4i4i0000000000000000000000000000000000
χ9344-4-4-4400040-4000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000-4-4444-4000-40400000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ9444-4-4-4400040-400000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000-4-4444-4000-404000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ9544-4-4-44000-404000000000000002-2-22-222-20000000000000000-4-4444-400040-400000000000000-222-22-2-220000000000000000
χ9644-4-4-44000-40400000000000000-222-22-2-220000000000000000-4-4444-400040-4000000000000002-2-22-222-20000000000000000
χ978-88-800000000000000004-40000000000000000000000000000-88-880000000000000000-440000000000000000000000000000
χ988-88-80000000000000000-440000000000000000000000000000-88-8800000000000000004-40000000000000000000000000000
χ998-8-88000000000000004-4000000000000000000000000000000-888-800000000000000-44000000000000000000000000000000
χ1008-8-8800000000000000-44000000000000000000000000000000-888-8000000000000004-4000000000000000000000000000000

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