Finite Group Databasebeta

← Group #72340407

Character table — Group #72340407

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97
size11112222222244444444444444444448888888888888888888888888888888816161616161616161616161616161616161616161616161616163232323232323232
order1222222222442222444444444444444222244444444444488888888888888882224444444444444444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111-1-1111111111111111111111-1-1-11-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111-1-1111111-1-111-1-1-1-11111111111111111-11-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-111-1-1-1-111-1-111111111-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111111111-1-1-1-1
χ91111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-111-1-1-11-1111111-1-1-1-1iiii−i−i−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-111-1-1-11-1111111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii
χ111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-11-11-11-1-1-1-1111111iiii−i−i−i−i−i−iii−i−iii
χ121111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-11-11-11-1-1-1-1111111−i−i−i−iiiiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-111-1-1111-1-1-1-1-1-111−i−i−i−iiiiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-111-1-1111-1-1-1-1-1-111iiii−i−i−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111iiiiiiii−i−i−i−i−i−i−i−i1-11-1111-1-1-111-1-111-1-1−i−i−i−iiiii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111−i−i−i−i−i−i−i−iiiiiiiii1-11-1111-1-1-111-1-111-1-1iiii−i−i−i−iii−i−i−i−iii
χ171111-1-1-1-111111-1-1111-1-11-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11-11-1-111-11-11-11-11-111-1-111-1-11-11-11-11-1
χ181111-1-1-1-111111-1-1111-1-11-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11-11-1-111-11-11-11-11-1-1-111-1-111-11-11-11-11
χ191111-1-1-1-111111-1-1111-1-11-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11111-1-11-111-1-11-1111-1-111-1-1-11-11-11-11
χ201111-1-1-1-111111-1-1111-1-11-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11111-1-11-111-1-11-11-1-111-1-1111-11-11-11-1
χ211111-1-1-1-111111-1-1111-1-11-1-1-1-1-1-11111-1-11111-1-11111-1-1111111-1-1-1-11111-1-1-1-11-1-11-1-11-11-1-11-111-1-11-1-111-1-1111-11-1-11-11
χ221111-1-1-1-111111-1-1111-1-11-1-1-1-1-1-11111-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-111111-1-11-1-11-11-1-11-111-1-1111-1-111-1-1-11-111-11-1
χ231111-1-1-1-111111-1-1111-1-11-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1111-1-11-11-111-1-11-111-1-1-111-1-111-11-111-11-1
χ241111-1-1-1-111111-1-1111-1-11-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111111-1-11-11-111-1-11-111-111-1-111-1-11-11-1-11-11
χ251111-1-1-1-111-1-1-111-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-111-11-1-11-11-11-1-11-11ii−i−i−i−iiii−i−iii−i−ii
χ261111-1-1-1-111-1-1-111-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-111-11-1-11-11-11-1-11-11−i−iiiii−i−i−iii−i−iii−i
χ271111-1-1-1-111-1-1-111-111-1-1-1111111-1-1-1-111-1-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111-11-111-11-11-1ii−i−i−i−iii−iii−i−iii−i
χ281111-1-1-1-111-1-1-111-111-1-1-1111111-1-1-1-111-1-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111-11-111-11-11-1−i−iiiii−i−ii−i−iii−i−ii
χ291111-1-1-1-111-1-1-111-111-1-1-1111111-1-1-1-1-1-11111-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1-11-11-111-1−i−iiiii−i−ii−i−ii−iii−i
χ301111-1-1-1-111-1-1-111-111-1-1-1111111-1-1-1-1-1-11111-1-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111-1-11-11-111-1ii−i−i−i−iii−iii−ii−i−ii
χ311111-1-1-1-111-1-1-111-111-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii-11111-1-1-1-111-1-111-1-11−i−iiiii−i−i−iii−ii−i−ii
χ321111-1-1-1-111-1-1-111-111-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11111-1-1-1-111-1-111-1-11ii−i−i−i−iiii−i−ii−iii−i
χ3322222222222222222222222-2-2-2-2-2-2-2-22200-2-2-2-22200-2-2-2-20000000000000000200020000000-2-200000000000000000000
χ3422222222222222222222222-2-2-2-2-2-2-2-2-2-200-2-2-2-2-2-20022220000000000000000-2000-200000002200000000000000000000
χ35222222222222-2-2-2-2-2-2-2-222222-2-222-2-200002-22-20000000000000000000000000022002200-2-20000-2-20000000000000000
χ36222222222222-2-2-2-2-2-2-2-222222-2-222-2-200002-22-200000000000000000000000000-2-200-2-200220000220000000000000000
χ37222222222222-2-2-2-2-2-2-2-2222-2-222-2-2220022-22-2200220000000000000000000002000200-2-20000-2-2000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2222-2-222-2-22200-2-2-22-2200-2-2000000000000000000000-2000-20022000022000000000000000000
χ392222222222-2-22222-2-2-2-2-2-2-222-2-222-2-20022-22-2200-2-20000000000000000000002000-200-2-2000022000000000000000000
χ402222222222-2-22222-2-2-2-2-2-2-222-2-222-2-200-2-2-22-220022000000000000000000000-2000200220000-2-2000000000000000000
χ412222222222-2-22222-2-2-2-2-2-2-2-2-222-2-22200002-22-2000000000000000000000000002-2002-200-2-20000220000000000000000
χ422222222222-2-22222-2-2-2-2-2-2-2-2-222-2-22200002-22-200000000000000000000000000-2200-2200220000-2-20000000000000000
χ432222222222-2-2-2-2-2-22222-2-2-2222222222200-2-2-2-2220022220000000000000000-2000-20000000-2-200000000000000000000
χ442222222222-2-2-2-2-2-22222-2-2-222222222-2-200-2-2-2-2-2-200-2-2-2-200000000000000002000200000002200000000000000000000
χ452222-2-2-2-222222-2-2222-2-22-2-22222-2-2-2-22200-2-222-2-200-2-2220000000000000000-200020000000-2200000000000000000000
χ462222-2-2-2-222222-2-2222-2-22-2-22222-2-2-2-2-2-200-2-222220022-2-200000000000000002000-200000002-200000000000000000000
χ472222-2-2-2-22222-222-2-2-2222-2-222-2-2-2-2220022-222-20022000000000000000000000-2000-200-220000-22000000000000000000
χ482222-2-2-2-22222-222-2-2-2222-2-222-2-2-2-22200-2-2-222-200-2-200000000000000000000020002002-200002-2000000000000000000
χ492222-2-2-2-22222-222-2-2-2222-2-2-2-22222-2-200002-2-22000000000000000000000000002-200-2200-220000-220000000000000000
χ502222-2-2-2-22222-222-2-2-2222-2-2-2-22222-2-200002-2-2200000000000000000000000000-22002-2002-200002-20000000000000000
χ512222-2-2-2-222-2-22-2-22-2-222-22222-2-2-2-22200002-2-22000000000000000000000000002200-2-200-2200002-20000000000000000
χ522222-2-2-2-222-2-22-2-22-2-222-22222-2-2-2-22200002-2-2200000000000000000000000000-2-20022002-20000-220000000000000000
χ532222-2-2-2-222-2-22-2-22-2-222-222-2-22222-2-20022-222-200-2-2000000000000000000000-2000200-2200002-2000000000000000000
χ542222-2-2-2-222-2-22-2-22-2-222-222-2-22222-2-200-2-2-222-200220000000000000000000002000-2002-20000-22000000000000000000
χ552222-2-2-2-222-2-2-222-222-2-2-222-2-2-2-222222200-2-222-2-20022-2-200000000000000002000-20000000-2200000000000000000000
χ562222-2-2-2-222-2-2-222-222-2-2-222-2-2-2-22222-2-200-2-2222200-2-2220000000000000000-2000200000002-200000000000000000000
χ572-22-222-2-22-20000002-22-20002i−2i2i−2i2i−2i2i−2i2-20000002-2002i−2i2i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ582-22-222-2-22-20000002-22-20002i−2i2i−2i2i−2i2i−2i2-20000002-2002i−2i2i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ592-22-222-2-22-20000002-22-20002i−2i2i−2i2i−2i2i−2i-22000000-2200−2i2i−2i2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ602-22-222-2-22-20000002-22-20002i−2i2i−2i2i−2i2i−2i-22000000-2200−2i2i−2i2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ612-22-222-2-22-20000002-22-2000−2i2i−2i2i−2i2i−2i2i2-20000002-200−2i2i−2i2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ622-22-222-2-22-20000002-22-2000−2i2i−2i2i−2i2i−2i2i2-20000002-200−2i2i−2i2i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ632-22-222-2-22-20000002-22-2000−2i2i−2i2i−2i2i−2i2i-22000000-22002i−2i2i−2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ642-22-222-2-22-20000002-22-2000−2i2i−2i2i−2i2i−2i2i-22000000-22002i−2i2i−2i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ652-22-2-2-2222-20000002-2-220002i−2i2i−2i−2i2i−2i2i2-2000000-2200−2i2i2i−2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ662-22-2-2-2222-20000002-2-220002i−2i2i−2i−2i2i−2i2i2-2000000-2200−2i2i2i−2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ672-22-2-2-2222-20000002-2-220002i−2i2i−2i−2i2i−2i2i-220000002-2002i−2i−2i2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ682-22-2-2-2222-20000002-2-220002i−2i2i−2i−2i2i−2i2i-220000002-2002i−2i−2i2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ692-22-2-2-2222-20000002-2-22000−2i2i−2i2i2i−2i2i−2i2-2000000-22002i−2i−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ702-22-2-2-2222-20000002-2-22000−2i2i−2i2i2i−2i2i−2i2-2000000-22002i−2i−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ712-22-2-2-2222-20000002-2-22000−2i2i−2i2i2i−2i2i−2i-220000002-200−2i2i2i−2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ722-22-2-2-2222-20000002-2-22000−2i2i−2i2i2i−2i2i−2i-220000002-200−2i2i2i−2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ7344444-44-4-4-44400000000-44-40000000000000000000000002-22-22-22-22-22-22-22-20000000000000000000000000000000000
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χ914-44-4-4-4444-4000000-444-40004i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ924-44-4-4-4444-4000000-444-4000−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-80000008i−8i0000000000000000000004-40000004i−4i000000000000000000000000000000000000000000000000000000
χ9488-8-80000008i−8i000000000000000000000-44000000−4i4i000000000000000000000000000000000000000000000000000000
χ9588-8-8000000−8i8i0000000000000000000004-4000000−4i4i000000000000000000000000000000000000000000000000000000
χ9688-8-8000000−8i8i000000000000000000000-440000004i−4i000000000000000000000000000000000000000000000000000000
χ9716-16-1616000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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