Finite Group Databasebeta

← Group #393012

Character table — Group #393012

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12224444222222222244444444448888888888888888224444444444444444448888888888888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-111111-1-1-1-1
χ911111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ1011111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ1111111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111-1-111
χ1211111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-111-1-1
χ1311111111111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1111-111-1-1-1-111
χ1411111111111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1111-1-1-11-1-11111-1-1
χ1511111111111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111-1-1-11111-1-1
χ1611111111111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-1-1-111
χ171111-1-1-1-111-111-1-1-1-1-1111-1-111-1-111111-1-1-1-11111-1-1-1-11-11-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1111-11-1-1-1i−ii−ii−ii−i
χ181111-1-1-1-111-111-1-1-1-1-1111-1-111-1-111111-1-1-1-11111-1-1-1-11-11-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1-1-1-11-1111−ii−ii−ii−ii
χ191111-1-1-1-111-111-1-1-1-1-1111-1-111-1-111111-1-1-1-11111-1-1-1-11-11-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1111-11-1-1-1−ii−ii−ii−ii
χ201111-1-1-1-111-111-1-1-1-1-1111-1-111-1-111111-1-1-1-11111-1-1-1-11-11-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1-1-1-11-1111i−ii−ii−ii−i
χ211111-1-1-1-111-111-1-1-1-1-1111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1111-11-1-11-11i−ii−i−ii−ii
χ221111-1-1-1-111-111-1-1-1-1-1111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111-11-111-11-1−ii−iii−ii−i
χ231111-1-1-1-111-111-1-1-1-1-1111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1111-11-1-11-11−ii−iii−ii−i
χ241111-1-1-1-111-111-1-1-1-1-1111-1-111-1-11-1-1-1-11111-1-1-1-111111-11-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111-11-111-11-1i−ii−i−ii−ii
χ251111-1-1-1-111-1-1-111-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-11-11iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-11111-11-11-1-1i−i−iii−i−ii
χ261111-1-1-1-111-1-1-111-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-11-11iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111-1-11-11-111−iii−i−iii−i
χ271111-1-1-1-111-1-1-111-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-11-11−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-11111-11-11-1-1−iii−i−iii−i
χ281111-1-1-1-111-1-1-111-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-11-11−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111-1-11-11-111i−i−iii−i−ii
χ291111-1-1-1-111-1-1-111-1-1-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-11-11iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-11-1-111-1-11i−i−ii−iii−i
χ301111-1-1-1-111-1-1-111-1-1-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-11-11iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-111-1-111-1−iii−ii−i−ii
χ311111-1-1-1-111-1-1-111-1-1-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-11-11−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-11-1-111-1-11−iii−ii−i−ii
χ321111-1-1-1-111-1-1-111-1-1-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-11-11−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-111-1-111-1i−i−ii−iii−i
χ332222222222-222-2-2-2-2-2-2-2-222-2-222-200000000000000002-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ342222222222-222-2-2-2-2-2-2-2-222-2-222-200000000000000002-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ352222222222-2-2-222-2-2-2-2-2-22222-2-2-20000000000000000-222-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ362222222222-2-2-222-2-2-2-2-2-22222-2-2-20000000000000000-222-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ3722222222-2-2222222-2-22-2-2-2-2222222222222222222222-2-2-2-200000000000000000000000000000000-2-2-2-2-2-2-2-20000000000000000
χ3822222222-2-2222222-2-22-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000222222220000000000000000
χ3922222222-2-22-2-2-2-22-2-22-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2-2-2-222220000000000000000
χ4022222222-2-22-2-2-2-22-2-22-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2222222222222000000000000000000000000000000002222-2-2-2-20000000000000000
χ4122222222-2-2-222-2-2-222-222-2-2-2-222-20000000000000000-222-2000000000000000022-2-222-2-222-2-222-2-2000000000000000000000000
χ4222222222-2-2-222-2-2-222-222-2-2-2-222-20000000000000000-222-20000000000000000-2-222-2-222-2-222-2-222000000000000000000000000
χ4322222222-2-2-2-2-222-222-222-2-222-2-2-200000000000000002-2-22000000000000000022-2-222-2-2-2-222-2-222000000000000000000000000
χ4422222222-2-2-2-2-222-222-222-2-222-2-2-200000000000000002-2-220000000000000000-2-222-2-22222-2-222-2-2000000000000000000000000
χ452222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ462222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2000000000000000022-2-2-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000
χ472222-2-2-2-2222-2-2-2-2222-2-2-2-2-22222-20000000000000000-2-22222-2-2-2-222-2-22222-2-20000000000000000000000000000000000000000
χ482222-2-2-2-2222-2-2-2-2222-2-2-2-2-22222-20000000000000000-2-222-2-22222-2-222-2-2-2-2220000000000000000000000000000000000000000
χ492222-2-2-2-2-2-2222222-2-2-22222-2-2-2-2-20000000000000000-2-22200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ502222-2-2-2-2-2-2222222-2-2-22222-2-2-2-2-20000000000000000-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ512222-2-2-2-2-2-22-2-2-2-22-2-2-222222222-2000000000000000022-2-200000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ522222-2-2-2-2-2-22-2-2-2-22-2-2-222222222-2000000000000000022-2-20000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ532222-2-2-2-2-2-2-222-2-2-2222-2-22222-2-222222-2-2-2-22222-2-2-2-2-22-2200000000000000000000000000000000-2-222-2-2220000000000000000
χ542222-2-2-2-2-2-2-222-2-2-2222-2-22222-2-22-2-2-2-22222-2-2-2-22222-22-220000000000000000000000000000000022-2-222-2-20000000000000000
χ552222-2-2-2-2-2-2-2-2-222-2222-2-222-2-22222222-2-2-2-2-2-2-2-222222-22-200000000000000000000000000000000-2-22222-2-20000000000000000
χ562222-2-2-2-2-2-2-2-2-222-2222-2-222-2-2222-2-2-2-222222222-2-2-2-22-22-20000000000000000000000000000000022-2-2-2-2220000000000000000
χ572-2-2222-2-22-220000-22-2-22-22-20000222-2-222-2-2000000000000000000002i−2i2i−2i2i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000
χ582-2-2222-2-22-220000-22-2-22-22-20000222-2-222-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000
χ592-2-2222-2-22-220000-22-2-22-22-200002-2-222-2-222000000000000000000002i−2i2i−2i2i−2i2i−2i00000000−2i2i−2i2i−2i2i−2i2i-22-2200000000000000000000
χ602-2-2222-2-22-220000-22-2-22-22-200002-2-222-2-22200000000000000000000−2i2i−2i2i−2i2i−2i2i000000002i−2i2i−2i2i−2i2i−2i-22-2200000000000000000000
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χ762-2-22-2-2222-220000-22-22-22-220000-200000000−2i−2i2i2i2i2i−2i−2i000000000000−2i2i2i−2i2i−2i−2i2i-22-222-22-2000000000000−2i2i2i−2i0000000000000000
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χ782-2-22-2-2222-2-200002-22-22-2-220000222-2-2-2-22200000000000000000000-22-222-22-200000000-22-222-22-22-2-2200000000000000000000
χ792-2-22-2-2222-2-200002-22-22-2-2200002-2-22222-2-2000000000000000000002-22-2-22-2200000000-22-222-22-2-222-200000000000000000000
χ802-2-22-2-2222-2-200002-22-22-2-2200002-2-22222-2-200000000000000000000-22-222-22-2000000002-22-2-22-22-222-200000000000000000000
χ812-2-22-2-222-2220000-2-2222-22-20000-2000000002i2i−2i−2i−2i−2i2i2i00002i−2i−2i2i−2i2i2i−2i0000000000000000-222-22-2-220000−2i2i2i−2i0000000000000000
χ822-2-22-2-222-2220000-2-2222-22-20000-2000000002i2i−2i−2i−2i−2i2i2i0000−2i2i2i−2i2i−2i−2i2i00000000000000002-2-22-222-20000−2i2i2i−2i0000000000000000
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χ882-2-22-2-222-22-2000022-2-2-222-200002-2-22222-2-2000000000000-22-222-22-2000000002-2-22-222-2000000002-2-2200000000000000000000
χ8944-4-44i−4i4i−4i000004-4000000004i−4i00022−2222−222i2−2i22i2−2i22i2−2i22i2−2i222−2222−22000000000000000000000000000000000000000000000000000000000000
χ9044-4-44i−4i4i−4i000004-4000000004i−4i000−2222−2222−2i22i2−2i22i2−2i22i2−2i22i2−2222−2222000000000000000000000000000000000000000000000000000000000000
χ9144-4-44i−4i4i−4i00000-4400000000−4i4i00022−2222−222i2−2i22i2−2i2−2i22i2−2i22i2−2222−2222000000000000000000000000000000000000000000000000000000000000
χ9244-4-44i−4i4i−4i00000-4400000000−4i4i000−2222−2222−2i22i2−2i22i22i2−2i22i2−2i222−2222−22000000000000000000000000000000000000000000000000000000000000
χ9344-4-4−4i4i−4i4i000004-400000000−4i4i00022−2222−22−2i22i2−2i22i2−2i22i2−2i22i222−2222−22000000000000000000000000000000000000000000000000000000000000
χ9444-4-4−4i4i−4i4i000004-400000000−4i4i000−2222−22222i2−2i22i2−2i22i2−2i22i2−2i2−2222−2222000000000000000000000000000000000000000000000000000000000000
χ9544-4-4−4i4i−4i4i00000-44000000004i−4i00022−2222−22−2i22i2−2i22i22i2−2i22i2−2i2−2222−2222000000000000000000000000000000000000000000000000000000000000
χ9644-4-4−4i4i−4i4i00000-44000000004i−4i000−2222−22222i2−2i22i2−2i2−2i22i2−2i22i222−2222−22000000000000000000000000000000000000000000000000000000000000
χ974-44-44i−4i−4i4i0004-40000000000004i−4i022−22−22222i2−2i2−2i22i222−22−2222−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ984-44-44i−4i−4i4i0004-40000000000004i−4i0−222222−22−2i22i22i2−2i2−222222−222i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ994-44-44i−4i−4i4i000-44000000000000−4i4i022−22−22222i2−2i2−2i22i2−222222−222i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ1004-44-44i−4i−4i4i000-44000000000000−4i4i0−222222−22−2i22i22i2−2i222−22−2222−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ1014-44-4−4i4i4i−4i0004-4000000000000−4i4i022−22−2222−2i22i22i2−2i222−22−22222i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ1024-44-4−4i4i4i−4i0004-4000000000000−4i4i0−222222−222i2−2i2−2i22i2−222222−22−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ1034-44-4−4i4i4i−4i000-440000000000004i−4i022−22−2222−2i22i22i2−2i2−222222−22−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ1044-44-4−4i4i4i−4i000-440000000000004i−4i0−222222−222i2−2i2−2i22i222−22−22222i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000

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