Finite Group Databasebeta

← Group #141048

Character table — Group #141048

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122222224444444444444444888888884444448888888888888888888888888888161616161616161616161616161616162244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-1
χ6111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-11-11
χ7111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-11-11
χ8111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1-11-1
χ911111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-11
χ1011111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1
χ1111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-111-1
χ1211111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-1-11
χ1311111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1411111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1611111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ17222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ18222222222222222222-2-2-2-22200000000-2-2-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ19222222222222222222-2-2-2-22200000000-2-2-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ20222222222222-2-2-2-2-2-22222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000
χ2322222222-2-2-2-22222-2-22222-2-222222222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-2220000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-2220000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000
χ2622222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-222000000002222-2-2000000000000000000000000000022−2−2−2−222−2−22222−2−20000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-222000000002222-2-20000000000000000000000000000−2−22222−2−222−2−2−2−2220000
χ292222-2-2-2-200002i2i−2i−2i0022-2-20022-2-222-2-2002i−2i0000002i2i−2i−2i0000i2i2−i2−i222−2−222−2−2i2i2−i2−i200000000000000000000
χ302222-2-2-2-200002i2i−2i−2i0022-2-20022-2-222-2-2002i−2i0000002i2i−2i−2i0000−i2−i2i2i2−2−222−2−222−i2−i2i2i200000000000000000000
χ312222-2-2-2-200002i2i−2i−2i0022-2-200-2-222-2-222002i−2i000000−2i−2i2i2i000022−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000000000000000
χ322222-2-2-2-200002i2i−2i−2i0022-2-200-2-222-2-222002i−2i000000−2i−2i2i2i0000−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000000000000000
χ332222-2-2-2-20000−2i−2i2i2i0022-2-20022-2-222-2-200−2i2i000000−2i−2i2i2i0000i2i2−i2−i2−2−222−2−222i2i2−i2−i200000000000000000000
χ342222-2-2-2-20000−2i−2i2i2i0022-2-20022-2-222-2-200−2i2i000000−2i−2i2i2i0000−i2−i2i2i222−2−222−2−2−i2−i2i2i200000000000000000000
χ352222-2-2-2-20000−2i−2i2i2i0022-2-200-2-222-2-22200−2i2i0000002i2i−2i−2i000022−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000000000000000
χ362222-2-2-2-20000−2i−2i2i2i0022-2-200-2-222-2-22200−2i2i0000002i2i−2i−2i0000−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000000000000000
χ3722-2-222-2-22i2i−2i−2i0000002-22-20022-2-2-2-2222i−2i0000000000002i2i−2i−2i2−22−2i2−i2i2−i2i2−i2i2−i22−22−200000000000000000000
χ3822-2-222-2-22i2i−2i−2i0000002-22-20022-2-2-2-2222i−2i0000000000002i2i−2i−2i−22−22−i2i2−i2i2−i2i2−i2i2−22−2200000000000000000000
χ3922-2-222-2-22i2i−2i−2i0000002-22-200-2-22222-2-22i−2i000000000000−2i−2i2i2ii2−i2i2−i2−22−222−22−2−i2i2−i2i200000000000000000000
χ4022-2-222-2-22i2i−2i−2i0000002-22-200-2-22222-2-22i−2i000000000000−2i−2i2i2i−i2i2−i2i22−22−2−22−22i2−i2i2−i200000000000000000000
χ4122-2-222-2-2−2i−2i2i2i0000002-22-20022-2-2-2-222−2i2i000000000000−2i−2i2i2i2−22−2−i2i2−i2i2−i2i2−i2i22−22−200000000000000000000
χ4222-2-222-2-2−2i−2i2i2i0000002-22-20022-2-2-2-222−2i2i000000000000−2i−2i2i2i−22−22i2−i2i2−i2i2−i2i2−i2−22−2200000000000000000000
χ4322-2-222-2-2−2i−2i2i2i0000002-22-200-2-22222-2-2−2i2i0000000000002i2i−2i−2ii2−i2i2−i22−22−2−22−22−i2i2−i2i200000000000000000000
χ4422-2-222-2-2−2i−2i2i2i0000002-22-200-2-22222-2-2−2i2i0000000000002i2i−2i−2i−i2i2−i2i2−22−222−22−2i2−i2i2−i200000000000000000000
χ4522-2-2-2-222000000002-22-2-222-22222-2-2-2-200002-222-2-20000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ4622-2-2-2-222000000002-22-2-222-22222-2-2-2-200002-222-2-2000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ4722-2-2-2-222000000002-22-2-222-2-2-2-2-2222200002-2-2-222000000002-2-2200000000-222-200000000000000000000
χ4822-2-2-2-222000000002-22-2-222-2-2-2-2-2222200002-2-2-22200000000-222-2000000002-2-2200000000000000000000
χ4922-2-2-2-22200000000-222-2-22-222222-2-2-2-20000-22-2-222000000002i−2i−2i2i000000002i−2i−2i2i00000000000000000000
χ5022-2-2-2-22200000000-222-2-22-222222-2-2-2-20000-22-2-22200000000−2i2i2i−2i00000000−2i2i2i−2i00000000000000000000
χ5122-2-2-2-22200000000-222-2-22-22-2-2-2-222220000-2222-2-20000000000002-2-22-222-2000000000000000000000000
χ5222-2-2-2-22200000000-222-2-22-22-2-2-2-222220000-2222-2-2000000000000-222-22-2-22000000000000000000000000
χ532-22-22-2-222-22-22-22-2220000-2-22−22−22−22−20000002−22−22−22−22−22−20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000
χ542-22-22-2-222-22-22-22-2220000-2-22−22−22−22−20000002−22−22−22−22−22−20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000
χ552-22-22-2-222-22-22-22-2220000-2-2−22−22−22−22000000−22−22−22−22−22−220000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000
χ562-22-22-2-222-22-22-22-2220000-2-2−22−22−22−22000000−22−22−22−22−22−220000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000
χ572-22-22-2-222-22-2-22-22-2-20000222−22−22−22−2000000−22−22−22−222−22−20000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ582-22-22-2-222-22-2-22-22-2-20000222−22−22−22−2000000−22−22−22−222−22−20000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ592-22-22-2-222-22-2-22-22-2-2000022−22−22−22−220000002−22−22−22−2−22−220000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ602-22-22-2-222-22-2-22-22-2-2000022−22−22−22−220000002−22−22−22−2−22−220000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ612-22-22-2-22-22-222-22-2-2-20000222−22−22−22−2000000−22−222−22−2−22−220000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ622-22-22-2-22-22-222-22-2-2-20000222−22−22−22−2000000−22−222−22−2−22−220000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ632-22-22-2-22-22-222-22-2-2-2000022−22−22−22−220000002−22−2−22−222−22−20000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ642-22-22-2-22-22-222-22-2-2-2000022−22−22−22−220000002−22−2−22−222−22−20000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ652-22-22-2-22-22-22-22-22220000-2-22−22−22−22−20000002−22−2−22−22−22−220000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000
χ662-22-22-2-22-22-22-22-22220000-2-22−22−22−22−20000002−22−2−22−22−22−220000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000
χ672-22-22-2-22-22-22-22-22220000-2-2−22−22−22−22000000−22−222−22−22−22−20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000
χ682-22-22-2-22-22-22-22-22220000-2-2−22−22−22−22000000−22−222−22−22−22−20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000
χ694444-4-4-4-400004i4i−4i−4i00-4-444000000000000−4i4i00000000000000000000000000000000000000000000000000
χ704444-4-4-4-40000−4i−4i4i4i00-4-4440000000000004i−4i00000000000000000000000000000000000000000000000000
χ7144-4-444-4-44i4i−4i−4i000000-44-440000000000−4i4i0000000000000000000000000000000000000000000000000000
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χ7344-4-4-4-444000000004-4-444-44-4000000000000-44000000000000000000000000000000000000000000000000
χ7444-4-4-4-44400000000-44-444-4-440000000000004-4000000000000000000000000000000000000000000000000
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χ774-44-4-444-40000−4i4i4i−4i0000000022−22−222222−22−22220000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ784-44-4-444-40000−4i4i4i−4i00000000−222222−22−222222−2200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ794-4-444-44-44i−4i−4i4i00000000000022−22−2222−222222−22000000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ804-4-444-44-44i−4i−4i4i000000000000−222222−2222−22−222200000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ814-4-444-44-4−4i4i4i−4i00000000000022−22−2222−222222−2200000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ824-4-444-44-4−4i4i4i−4i000000000000−222222−2222−22−2222000000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ834-4-44-44-44000000004-40000-4422−2222−22−2222−222200000022−22−222200000000000000000000000000000000000000000000
χ844-4-44-44-44000000004-40000-44−2222−222222−2222−22000000−222222−2200000000000000000000000000000000000000000000
χ854-4-44-44-4400000000-4400004-422−2222−22−2222−2222000000−222222−2200000000000000000000000000000000000000000000
χ864-4-44-44-4400000000-4400004-4−2222−222222−2222−2200000022−22−222200000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.