Finite Group Databasebeta

← Group #213129

Character table — Group #213129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444444444444444448888888888888888444488888888888888888888888888888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ17111-1-1-11-1ii−i−iii−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-1i−ii−i1-11-1i−ii−i1-1
χ18111-1-1-11-1ii−i−iii−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11−ii−ii-11-11−ii−ii-11
χ19111-1-1-11-1ii−i−iii−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111111-1i−ii−i1-1-11−ii−ii-11
χ20111-1-1-11-1ii−i−iii−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-11−ii−ii-111-1i−ii−i1-1
χ21111-1-1-11-1ii−i−iii−i−i1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1−iii−i-111-1i−i−ii-11
χ22111-1-1-11-1ii−i−iii−i−i1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11i−i−ii1-1-11−iii−i1-1
χ23111-1-1-11-1ii−i−iii−i−i1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-11-1−iii−i-11-11−iii−i1-1
χ24111-1-1-11-1ii−i−iii−i−i1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-11i−i−ii1-11-1i−i−ii-11
χ25111-1-1-11-1−i−iii−i−iii1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111-1i−i−ii-111-1−iii−i-11
χ26111-1-1-11-1−i−iii−i−iii1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11−iii−i1-1-11i−i−ii1-1
χ27111-1-1-11-1−i−iii−i−iii1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-11-1i−i−ii-11-11i−i−ii1-1
χ28111-1-1-11-1−i−iii−i−iii1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-11−iii−i1-11-1−iii−i-11
χ29111-1-1-11-1−i−iii−i−iii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-1−ii−ii1-11-1−ii−ii1-1
χ30111-1-1-11-1−i−iii−i−iii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-11i−ii−i-11-11i−ii−i-11
χ31111-1-1-11-1−i−iii−i−iii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111111-1−ii−ii1-1-11i−ii−i-11
χ32111-1-1-11-1−i−iii−i−iii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-11i−ii−i-111-1−ii−ii1-1
χ332222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-222-2-222-2-2-2-2-2-200000000000000002-22-200000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ36222222222222-2-2-2-222-2-222-2-2-2-2-2-200000000000000002-22-2000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ37222222222222-2-2-2-2-2-222-2-222-2-2-2-20000000000000000-22-220000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ38222222222222-2-2-2-2-2-222-2-222-2-2-2-20000000000000000-22-2200000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3922222222-2-2-2-2222222-2-222-2-2-2-2-2-20000000000000000-22-2200000000000000000000000022-2-222-2-2-2-222-2-2220000000000000000
χ4022222222-2-2-2-2222222-2-222-2-2-2-2-2-20000000000000000-22-22000000000000000000000000-2-222-2-22222-2-222-2-20000000000000000
χ4122222222-2-2-2-22222-2-222-2-222-2-2-2-200000000000000002-22-20000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ4222222222-2-2-2-22222-2-222-2-222-2-2-2-200000000000000002-22-200000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-22222-2-222-2-222000000000000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222222222-2-222-2-2000000000000000000000000000000000000000000000000
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χ55222-2-2-22-2−2i−2i2i2i−2i−2i2i2i-2-2-2-2222222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i-2-22222-2-2000000000000000000000000000000000000000000000000
χ56222-2-2-22-2−2i−2i2i2i−2i−2i2i2i-2-2-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i22-2-2-2-222000000000000000000000000000000000000000000000000
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χ702-2-222-22-2−2i2i−2i2i−2i2i−2i2i000000002-22-200002i2i−2i−2i00002i2i−2i−2i000000-2200-22−22−22−22−22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
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χ722-2-222-22-2−2i2i−2i2i−2i2i−2i2i000000002-22-20000−2i−2i2i2i0000−2i−2i2i2i0000002-2002-2−22−22−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ732-2-2-2-22222-2-222-2-22000000002-2-22000022-2-20000-2-2220000002-200-222−22−2−22−222−22−2−22−222−22−2−22−222−22−2−22−220000000000000000
χ742-2-2-2-22222-2-222-2-22000000002-2-22000022-2-20000-2-2220000002-200-22−22−222−22−2−22−222−22−2−22−222−22−2−22−222−22−20000000000000000
χ752-2-2-2-22222-2-222-2-22000000002-2-220000-2-222000022-2-2000000-22002-22−22−2−22−222−22−2−22−22−22−222−22−2−22−222−22−20000000000000000
χ762-2-2-2-22222-2-222-2-22000000002-2-220000-2-222000022-2-2000000-22002-2−22−222−22−2−22−222−22−22−22−2−22−222−22−2−22−220000000000000000
χ772-2-2-2-22222-2-22-222-200000000-222-222-2-20000-2-222000000002-200-22002−2−22−222−22−2−22−222−22−2−22−222−22−2−22−222−20000000000000000
χ782-2-2-2-22222-2-22-222-200000000-222-222-2-20000-2-222000000002-200-2200−222−22−2−22−222−22−2−22−222−22−2−22−222−22−2−220000000000000000
χ792-2-2-2-22222-2-22-222-200000000-222-2-2-222000022-2-200000000-22002-2002−2−22−222−22−2−22−222−2−222−22−2−22−222−22−2−220000000000000000
χ802-2-2-2-22222-2-22-222-200000000-222-2-2-222000022-2-200000000-22002-200−222−22−2−22−222−22−2−222−2−22−222−22−2−22−222−20000000000000000
χ812-2-2-2-2222-222-22-2-2200000000-222-222-2-20000-2-22200000000-22002-2002−2−22−222−2−222−22−2−222−2−22−222−2−222−22−2−220000000000000000
χ822-2-2-2-2222-222-22-2-2200000000-222-222-2-20000-2-22200000000-22002-200−222−22−2−222−2−22−222−2−222−22−2−222−2−22−222−20000000000000000
χ832-2-2-2-2222-222-22-2-2200000000-222-2-2-222000022-2-2000000002-200-22002−2−22−222−2−222−22−2−22−222−22−2−222−2−22−222−20000000000000000
χ842-2-2-2-2222-222-22-2-2200000000-222-2-2-222000022-2-2000000002-200-2200−222−22−2−222−2−22−222−22−2−22−222−2−222−22−2−220000000000000000
χ852-2-2-2-2222-222-2-222-2000000002-2-22000022-2-20000-2-222000000-22002-22−22−2−22−22−22−222−22−22−22−2−22−22−22−222−22−20000000000000000
χ862-2-2-2-2222-222-2-222-2000000002-2-22000022-2-20000-2-222000000-22002-2−22−222−22−22−22−2−22−22−22−222−22−22−22−2−22−220000000000000000
χ872-2-2-2-2222-222-2-222-2000000002-2-220000-2-222000022-2-20000002-200-222−22−2−22−22−22−222−22−2−22−222−22−22−22−2−22−220000000000000000
χ882-2-2-2-2222-222-2-222-2000000002-2-220000-2-222000022-2-20000002-200-22−22−222−22−22−22−2−22−222−22−2−22−22−22−222−22−20000000000000000
χ8944-44-44-4-400000000004-4004-4000022−2222−2222−2222−2222−2222−2222−2222−22000000000000000000000000000000000000000000000000000000000000
χ9044-44-44-4-400000000004-4004-40000−2222−2222−2222−2222−2222−2222−2222−2222000000000000000000000000000000000000000000000000000000000000
χ9144-44-44-4-40000000000-4400-44000022−2222−22−2222−222222−2222−22−2222−2222000000000000000000000000000000000000000000000000000000000000
χ9244-44-44-4-40000000000-4400-440000−2222−222222−2222−22−2222−222222−2222−22000000000000000000000000000000000000000000000000000000000000
χ9344-4-44-4-4400000000004-400-4400002i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-4-4400000000004-400-440000−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-440000000000-44004-400002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-440000000000-44004-40000−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-44000000004-4004-40000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-44000000004-4004-4000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ994-444-4-4-4400000000-4400-440000002i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-4-4400000000-4400-44000000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ1014-44-444-4-4000000004-400-4400000022−22−222222−22−2222−222222−22−222222−22000000000000000000000000000000000000000000000000000000000000
χ1024-44-444-4-4000000004-400-44000000−222222−22−222222−2222−22−222222−22−2222000000000000000000000000000000000000000000000000000000000000
χ1034-44-444-4-400000000-44004-400000022−22−2222−222222−22−222222−2222−22−2222000000000000000000000000000000000000000000000000000000000000
χ1044-44-444-4-400000000-44004-4000000−222222−2222−22−222222−22−2222−222222−22000000000000000000000000000000000000000000000000000000000000

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