Finite Group Databasebeta

← Group #72321226

Character table — Group #72321226

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size11222222244444444444444888888816161616161616161616161616161616323232321122222224444444444444488888881616161616161616161616161616161632323232
order12244888824444488881616161681616161616161616161616161616323232323232323224442224488882444448888161616168161616161616161616161616161632323232323232322444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ6111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111
χ7111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ8111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ911111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111ii−i−iii−i−iii−i−iii−i−i1-11-111111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111ii−i−iii−i−iii−i−iii−i−i1-11-1
χ1011111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111ii−i−iii−i−i−i−iii−i−iii-11-1111111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111ii−i−iii−i−i−i−iii−i−iii-11-11
χ1111111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111−i−iii−i−iiiii−i−iii−i−i-11-1111111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111−i−iii−i−iiiii−i−iii−i−i-11-11
χ1211111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111−i−iii−i−iii−i−iii−i−iii1-11-111111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111−i−iii−i−iii−i−iii−i−iii1-11-1
χ1311111-1-111-1-1-1-111-11111111-1-1-111-1-111-1-1-1-11111-1-1-1-1111-1-1111111-1-111-1-1-1-111-11111111-1-1-111-1-111-1-1-1-11111-1-1-1-1111-1-11
χ1411111-1-111-1-1-1-111-11111111-1-1-111-1-111-1-1-1-111-1-11111-1-1-111-111111-1-111-1-1-1-111-11111111-1-1-111-1-111-1-1-1-111-1-11111-1-1-111-1
χ1511111-1-111-1-1-1-111-11111111-1-1-111-1-1-1-11111-1-111-1-1-1-111-111-111111-1-111-1-1-1-111-11111111-1-1-111-1-1-1-11111-1-111-1-1-1-111-111-1
χ1611111-1-111-1-1-1-111-11111111-1-1-111-1-1-1-11111-1-1-1-11111-1-11-1-1111111-1-111-1-1-1-111-11111111-1-1-111-1-1-1-11111-1-1-1-11111-1-11-1-11
χ172222222222222222222-2-2-2-22-2-2-2-2-2-2000000000000000000002222222222222222222-2-2-2-22-2-2-2-2-2-200000000000000000000
χ18222222222-2-222-2-222-2-22222-2-2-2-2-22200000000000000000000222222222-2-222-2-222-2-22222-2-2-2-2-22200000000000000000000
χ192222222-2-222-2-2-2-22-2220000-2000000000000002−22−22−22−200002222222-2-222-2-2-2-22-2220000-2000000000000002−22−22−22−20000
χ202222222-2-222-2-2-2-22-2220000-200000000000000−22−22−22−2200002222222-2-222-2-2-2-22-2220000-200000000000000−22−22−22−220000
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χ222222222-2-2-2-2-2-2222-2-2-20000200000000000000−i2i2−i2i2i2−i2i2−i200002222222-2-2-2-2-2-2222-2-2-20000200000000000000−i2i2−i2i2i2−i2i2−i20000
χ2322222-2-22222-2-2-2-2-22-2-22222222-2-2-2-20000000000000000000022222-2-22222-2-2-2-2-22-2-22222222-2-2-2-200000000000000000000
χ2422222-2-222-2-2-2-222-2222-2-2-2-2-222-2-2220000000000000000000022222-2-222-2-2-2-222-2222-2-2-2-2-222-2-22200000000000000000000
χ2522222-2-2-2-2222222-2-2-2-20000-200000000000000i2−i2−i2i2i2−i2−i2i2000022222-2-2-2-2222222-2-2-2-20000-200000000000000i2−i2−i2i2i2−i2−i2i20000
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χ2722222-2-2-2-2-2-222-2-2-2-22200002000000000000002−2−22−222−2000022222-2-2-2-2-2-222-2-2-2-22200002000000000000002−2−22−222−20000
χ2822222-2-2-2-2-2-222-2-2-2-2220000200000000000000−222−22−2−22000022222-2-2-2-2-2-222-2-2-2-2220000200000000000000−222−22−2−220000
χ2922-22-200-2-200002i−2i022i−2i2i2i−2i−2i0002-200002ζ3−2ζ32ζ−2ζ0000000000000022-22-200-2-200002i−2i022i−2i2i2i−2i−2i0002-200002ζ3−2ζ32ζ−2ζ00000000000000
χ3022-22-200-2-200002i−2i022i−2i2i2i−2i−2i0002-20000−2ζ32ζ3−2ζ2ζ0000000000000022-22-200-2-200002i−2i022i−2i2i2i−2i−2i0002-20000−2ζ32ζ3−2ζ2ζ00000000000000
χ3122-22-200-2-200002i−2i022i−2i−2i−2i2i2i000-22002ζ−2ζ00002ζ3−2ζ300000000000022-22-200-2-200002i−2i022i−2i−2i−2i2i2i000-22002ζ−2ζ00002ζ3−2ζ3000000000000
χ3222-22-200-2-200002i−2i022i−2i−2i−2i2i2i000-2200−2ζ2ζ0000−2ζ32ζ300000000000022-22-200-2-200002i−2i022i−2i−2i−2i2i2i000-2200−2ζ2ζ0000−2ζ32ζ3000000000000
χ3322-22-200-2-20000−2i2i02−2i2i2i2i−2i−2i000-22002ζ3−2ζ300002ζ−2ζ00000000000022-22-200-2-20000−2i2i02−2i2i2i2i−2i−2i000-22002ζ3−2ζ300002ζ−2ζ000000000000
χ3422-22-200-2-20000−2i2i02−2i2i2i2i−2i−2i000-2200−2ζ32ζ30000−2ζ2ζ00000000000022-22-200-2-20000−2i2i02−2i2i2i2i−2i−2i000-2200−2ζ32ζ30000−2ζ2ζ000000000000
χ3522-22-200-2-20000−2i2i02−2i2i−2i−2i2i2i0002-200002ζ−2ζ2ζ3−2ζ30000000000000022-22-200-2-20000−2i2i02−2i2i−2i−2i2i2i0002-200002ζ−2ζ2ζ3−2ζ300000000000000
χ3622-22-200-2-20000−2i2i02−2i2i−2i−2i2i2i0002-20000−2ζ2ζ−2ζ32ζ30000000000000022-22-200-2-20000−2i2i02−2i2i−2i−2i2i2i0002-20000−2ζ2ζ−2ζ32ζ300000000000000
χ37444-4-400004-40000000022−2222−22022−22000000000000000000000000444-4-400004-40000000022−2222−22022−22000000000000000000000000
χ38444-4-400004-400000000−2222−22220−2222000000000000000000000000444-4-400004-400000000−2222−22220−2222000000000000000000000000
χ39444-4-40000-440000000022−2222−220−2222000000000000000000000000444-4-40000-440000000022−2222−220−2222000000000000000000000000
χ40444-4-40000-4400000000−2222−2222022−22000000000000000000000000444-4-40000-4400000000−2222−2222022−22000000000000000000000000
χ4144-44-4004400004i−4i0-4−4i4i000000000000000000000000000000044-44-4004400004i−4i0-4−4i4i0000000000000000000000000000000
χ4244-44-400440000−4i4i0-44i−4i000000000000000000000000000000044-44-400440000−4i4i0-44i−4i0000000000000000000000000000000
χ4344-4-444400000000-40002i2−2i2−2i22i2000002i2−2i20000000000000000000044-4-444400000000-40002i2−2i2−2i22i2000002i2−2i200000000000000000000
χ4444-4-444400000000-4000−2i22i22i2−2i200000−2i22i20000000000000000000044-4-444400000000-4000−2i22i22i2−2i200000−2i22i200000000000000000000
χ4544-4-44-4-40000000040002i2−2i2−2i22i200000−2i22i20000000000000000000044-4-44-4-40000000040002i2−2i2−2i22i200000−2i22i200000000000000000000
χ4644-4-44-4-4000000004000−2i22i22i2−2i2000002i2−2i20000000000000000000044-4-44-4-4000000004000−2i22i22i2−2i2000002i2−2i200000000000000000000
χ478-80004i2−4i242−42004i−4i00000000000000000000000000000000000008-80004i2−4i242−42004i−4i0000000000000000000000000000000000000
χ488-80004i2−4i2−424200−4i4i00000000000000000000000000000000000008-80004i2−4i2−424200−4i4i0000000000000000000000000000000000000
χ498-8000−4i24i242−4200−4i4i00000000000000000000000000000000000008-8000−4i24i242−4200−4i4i0000000000000000000000000000000000000
χ508-8000−4i24i2−4242004i−4i00000000000000000000000000000000000008-8000−4i24i2−4242004i−4i0000000000000000000000000000000000000
χ5111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ53111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ54111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ55111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111
χ56111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-1-1-1-1-1-111-1-111-1-11111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1
χ57111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-1-1-1-1-1-111-1-111-1-11111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1
χ58111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111
χ5911111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111ii−i−iii−i−iii−i−iii−i−i1-11-1-1-1-1-1-111-1-1-1-111111-1111111-111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-11-11
χ6011111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111ii−i−iii−i−i−i−iii−i−iii-11-11-1-1-1-1-111-1-1-1-111111-1111111-111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i1-11-1
χ6111111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111−i−iii−i−iiiii−i−iii−i−i-11-11-1-1-1-1-111-1-1-1-111111-1111111-111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii1-11-1
χ6211111-1-11111-1-1-1-1-11-1-1-1-1-1-11-1-11111−i−iii−i−iii−i−iii−i−iii1-11-1-1-1-1-1-111-1-1-1-111111-1111111-111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-11-11
χ6311111-1-111-1-1-1-111-11111111-1-1-111-1-111-1-1-1-11111-1-1-1-1111-1-11-1-1-1-1-111-1-11111-1-11-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1-111-1
χ6411111-1-111-1-1-1-111-11111111-1-1-111-1-111-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-111-1-11111-1-11-1-1-1-1-1-1-1111-1-111-1-11111-1-111-1-1-1-1111-1-11
χ6511111-1-111-1-1-1-111-11111111-1-1-111-1-1-1-11111-1-111-1-1-1-111-111-1-1-1-1-1-111-1-11111-1-11-1-1-1-1-1-1-1111-1-11111-1-1-1-111-1-11111-1-11-1-11
χ6611111-1-111-1-1-1-111-11111111-1-1-111-1-1-1-11111-1-1-1-11111-1-11-1-11-1-1-1-1-111-1-11111-1-11-1-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-111-111-1
χ672222222222222222222-2-2-2-22-2-2-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-222222200000000000000000000
χ68222222222-2-222-2-222-2-22222-2-2-2-2-22200000000000000000000-2-2-2-2-2-2-2-2-222-2-222-2-222-2-2-2-222222-2-200000000000000000000
χ692222222-2-222-2-2-2-22-2220000-2000000000000002−22−22−22−20000-2-2-2-2-2-2-222-2-22222-22-2-20000200000000000000−22−22−22−220000
χ702222222-2-222-2-2-2-22-2220000-200000000000000−22−22−22−220000-2-2-2-2-2-2-222-2-22222-22-2-200002000000000000002−22−22−22−20000
χ712222222-2-2-2-2-2-2222-2-2-20000200000000000000i2−i2i2−i2−i2i2−i2i20000-2-2-2-2-2-2-2222222-2-2-22220000-200000000000000−i2i2−i2i2i2−i2i2−i20000
χ722222222-2-2-2-2-2-2222-2-2-20000200000000000000−i2i2−i2i2i2−i2i2−i20000-2-2-2-2-2-2-2222222-2-2-22220000-200000000000000i2−i2i2−i2−i2i2−i2i20000
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χ7422222-2-222-2-2-2-222-2222-2-2-2-2-222-2-22200000000000000000000-2-2-2-2-222-2-22222-2-22-2-2-222222-2-222-2-200000000000000000000
χ7522222-2-2-2-2222222-2-2-2-20000-200000000000000i2−i2−i2i2i2−i2−i2i20000-2-2-2-2-22222-2-2-2-2-2-222220000200000000000000−i2i2i2−i2−i2i2i2−i20000
χ7622222-2-2-2-2222222-2-2-2-20000-200000000000000−i2i2i2−i2−i2i2i2−i20000-2-2-2-2-22222-2-2-2-2-2-222220000200000000000000i2−i2−i2i2i2−i2−i2i20000
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χ7822222-2-2-2-2-2-222-2-2-2-2220000200000000000000−222−22−2−220000-2-2-2-2-2222222-2-22222-2-20000-2000000000000002−2−22−222−20000
χ7922-22-200-2-200002i−2i022i−2i2i2i−2i−2i0002-200002ζ3−2ζ32ζ−2ζ00000000000000-2-22-2200220000−2i2i0-2−2i2i−2i−2i2i2i000-220000−2ζ32ζ3−2ζ2ζ00000000000000
χ8022-22-200-2-200002i−2i022i−2i2i2i−2i−2i0002-20000−2ζ32ζ3−2ζ2ζ00000000000000-2-22-2200220000−2i2i0-2−2i2i−2i−2i2i2i000-2200002ζ3−2ζ32ζ−2ζ00000000000000
χ8122-22-200-2-200002i−2i022i−2i−2i−2i2i2i000-22002ζ−2ζ00002ζ3−2ζ3000000000000-2-22-2200220000−2i2i0-2−2i2i2i2i−2i−2i0002-200−2ζ2ζ0000−2ζ32ζ3000000000000
χ8222-22-200-2-200002i−2i022i−2i−2i−2i2i2i000-2200−2ζ2ζ0000−2ζ32ζ3000000000000-2-22-2200220000−2i2i0-2−2i2i2i2i−2i−2i0002-2002ζ−2ζ00002ζ3−2ζ3000000000000
χ8322-22-200-2-20000−2i2i02−2i2i2i2i−2i−2i000-22002ζ3−2ζ300002ζ−2ζ000000000000-2-22-22002200002i−2i0-22i−2i−2i−2i2i2i0002-200−2ζ32ζ30000−2ζ2ζ000000000000
χ8422-22-200-2-20000−2i2i02−2i2i2i2i−2i−2i000-2200−2ζ32ζ30000−2ζ2ζ000000000000-2-22-22002200002i−2i0-22i−2i−2i−2i2i2i0002-2002ζ3−2ζ300002ζ−2ζ000000000000
χ8522-22-200-2-20000−2i2i02−2i2i−2i−2i2i2i0002-200002ζ−2ζ2ζ3−2ζ300000000000000-2-22-22002200002i−2i0-22i−2i2i2i−2i−2i000-220000−2ζ2ζ−2ζ32ζ300000000000000
χ8622-22-200-2-20000−2i2i02−2i2i−2i−2i2i2i0002-20000−2ζ2ζ−2ζ32ζ300000000000000-2-22-22002200002i−2i0-22i−2i2i2i−2i−2i000-2200002ζ−2ζ2ζ3−2ζ300000000000000
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χ90444-4-40000-4400000000−2222−2222022−22000000000000000000000000-4-4-44400004-40000000022−2222−220−2222000000000000000000000000
χ9144-44-4004400004i−4i0-4−4i4i0000000000000000000000000000000-4-44-4400-4-40000−4i4i044i−4i0000000000000000000000000000000
χ9244-44-400440000−4i4i0-44i−4i0000000000000000000000000000000-4-44-4400-4-400004i−4i04−4i4i0000000000000000000000000000000
χ9344-4-444400000000-40002i2−2i2−2i22i2000002i2−2i200000000000000000000-4-444-4-4-4000000004000−2i22i22i2−2i200000−2i22i200000000000000000000
χ9444-4-444400000000-4000−2i22i22i2−2i200000−2i22i200000000000000000000-4-444-4-4-40000000040002i2−2i2−2i22i2000002i2−2i200000000000000000000
χ9544-4-44-4-40000000040002i2−2i2−2i22i200000−2i22i200000000000000000000-4-444-44400000000-4000−2i22i22i2−2i2000002i2−2i200000000000000000000
χ9644-4-44-4-4000000004000−2i22i22i2−2i2000002i2−2i200000000000000000000-4-444-44400000000-40002i2−2i2−2i22i200000−2i22i200000000000000000000
χ978-80004i2−4i242−42004i−4i0000000000000000000000000000000000000-88000−4i24i2−424200−4i4i0000000000000000000000000000000000000
χ988-80004i2−4i2−424200−4i4i0000000000000000000000000000000000000-88000−4i24i242−42004i−4i0000000000000000000000000000000000000
χ998-8000−4i24i242−4200−4i4i0000000000000000000000000000000000000-880004i2−4i2−4242004i−4i0000000000000000000000000000000000000
χ1008-8000−4i24i2−4242004i−4i0000000000000000000000000000000000000-880004i2−4i242−4200−4i4i0000000000000000000000000000000000000

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