Finite Group Databasebeta

← Group #72322002

Character table — Group #72322002

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176
size111122222222224444444444444444444444444488888888888888881616161616161616161616161616161632323232323232323232323232323232111122222222224444444444444444444444444488888888888888881616161616161616161616161616161632323232323232323232323232323232
order12442224448888224444448888888888161616161616161644881616161616161616161616163232323232323232323232323232323224448888888888882244222444888822444444888888888816161616161616164488161616161616161616161616323232323232323232323232323232322444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ911111111111111-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-111111111111111-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ1011111111111111-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111111111111111-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ1111111111111111-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-11111111111111111-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1211111111111111-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-111111111111111-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ1311111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1ii−i−i−i−iii11111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1ii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i11111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−i−iiiii−i−i11111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111ii−i−i−i−iii11111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111ii−i−i−i−iii
χ1722222222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022222222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-222222-2-2-2-2222222222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000222222222222222222-2-2-2-222222-2-2-2-2222222222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1922222222222222-2-2-2-222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000022222222222222-2-2-2-222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2022222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-22222222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000022222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-22222222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ212222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-20000000022-2-200000000000022−2−222−2−222−2−222−2−200000000000000002222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-20000000022-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-20000000022-2-2000000000000−2−222−2−222−2−222−2−22200000000000000002222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-20000000022-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ232222222222-2-2-2-22222-2-2-2-2-2-2-2-2-22222-200000000-2-222000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000002222222222-2-2-2-22222-2-2-2-2-2-2-2-2-22222-200000000-2-222000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ242222222222-2-2-2-22222-2-2-2-2-2-2-2-2-22222-200000000-2-222000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000002222222222-2-2-2-22222-2-2-2-2-2-2-2-2-22222-200000000-2-222000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ252222222222-2-2-2-2-2-2-2-22222-22222-2-2-2-2-200000000-2-22200000000000022−2−2−2−22222−2−2−2−22200000000000000002222222222-2-2-2-2-2-2-2-22222-22222-2-2-2-2-200000000-2-22200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ262222222222-2-2-2-2-2-2-2-22222-22222-2-2-2-2-200000000-2-222000000000000−2−22222−2−2−2−22222−2−200000000000000002222222222-2-2-2-2-2-2-2-22222-22222-2-2-2-2-200000000-2-222000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ272222222222-2-2-2-2-2-2-2-2-2-2-2-2-222222222-20000000022-2-2000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000002222222222-2-2-2-2-2-2-2-2-2-2-2-2-222222222-20000000022-2-2000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
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χ3622222-2-2-22-222220000−2i2i−2i2i-20000−2i−2i2i2i-2000000000000-2-22200002i2i−2i−2i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i000000000000000022222-2-2-22-222220000−2i2i−2i2i-20000−2i−2i2i2i-2000000000000-2-22200002i2i−2i−2i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i0000000000000000
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χ3922222-2-2-22-2-2-2-2-200002i−2i2i−2i20000−2i−2i2i2i2−2i−2i−2i−2i2i2i2i2i00000000-2-22200002ζ−2ζ−2ζ2ζ0000−2ζ32ζ32ζ3−2ζ30000000000000000000022222-2-2-22-2-2-2-2-200002i−2i2i−2i20000−2i−2i2i2i2−2i−2i−2i−2i2i2i2i2i00000000-2-22200002ζ−2ζ−2ζ2ζ0000−2ζ32ζ32ζ3−2ζ300000000000000000000
χ4022222-2-2-22-2-2-2-2-200002i−2i2i−2i20000−2i−2i2i2i2−2i−2i−2i−2i2i2i2i2i00000000-2-2220000−2ζ2ζ2ζ−2ζ00002ζ3−2ζ3−2ζ32ζ30000000000000000000022222-2-2-22-2-2-2-2-200002i−2i2i−2i20000−2i−2i2i2i2−2i−2i−2i−2i2i2i2i2i00000000-2-2220000−2ζ2ζ2ζ−2ζ00002ζ3−2ζ3−2ζ32ζ300000000000000000000
χ4122222-2-2-22-2-2-2-2-20000−2i2i−2i2i200002i2i−2i−2i22i2i2i2i−2i−2i−2i−2i00000000-2-22200002ζ3−2ζ3−2ζ32ζ30000−2ζ2ζ2ζ−2ζ0000000000000000000022222-2-2-22-2-2-2-2-20000−2i2i−2i2i200002i2i−2i−2i22i2i2i2i−2i−2i−2i−2i00000000-2-22200002ζ3−2ζ3−2ζ32ζ30000−2ζ2ζ2ζ−2ζ00000000000000000000
χ4222222-2-2-22-2-2-2-2-20000−2i2i−2i2i200002i2i−2i−2i22i2i2i2i−2i−2i−2i−2i00000000-2-2220000−2ζ32ζ32ζ3−2ζ300002ζ−2ζ−2ζ2ζ0000000000000000000022222-2-2-22-2-2-2-2-20000−2i2i−2i2i200002i2i−2i−2i22i2i2i2i−2i−2i−2i−2i00000000-2-2220000−2ζ32ζ32ζ3−2ζ300002ζ−2ζ−2ζ2ζ00000000000000000000
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χ1748-8−8i8i00000042−42−4i24i2-444i−4i000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000000000000000000-888i−8i000000−42424i2−4i24-4−4i4i00000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000000000000000000
χ1758-8−8i8i000000−42424i2−4i24-4−4i4i000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000000000000000000-888i−8i00000042−42−4i24i2-444i−4i00000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000000000000000000
χ1768-8−8i8i000000−42424i2−4i2-444i−4i00000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000000000000000000-888i−8i00000042−42−4i24i24-4−4i4i000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.