Finite Group Databasebeta

← Group #11779315

Character table — Group #11779315

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444488888888888888888888888121212121212121212121212121212122424242424242424242448484872727272
order122233444466666612121212346661212121212121212121212128812121212122424242424242424242424242424242422228888242424242424242444666612121212412122288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-11111111111111-111-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1
χ61111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1111-1-111
χ71111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-11-1-111-1-111-1-1-1-1-111
χ81111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111-1-1
χ92222222-22-222222222222-22222-2-2-2-222222-2-200-2-2-2-2-2000000000000000000220000000000000-2002200-2-20000000
χ102222222-22-222222222222-22222-2-2-2-222222-2-200-2-2-2-2-2000000000000000000-2-20000000000000200-2-200220000000
χ11222222-22-22222222-2-2-2-22-2222-22222-2-2-2-2-2-2-200-222-2-200000000000000002200000000000000-202200-2-2000000000
χ12222222-22-22222222-2-2-2-22-2222-22222-2-2-2-2-2-2-200-222-2-20000000000000000-2-20000000000000020-2-20022000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-222002-2-2220000000000000000000000000000000000000000000002-200
χ14222222-2-2-2-2222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-222002-2-222000000000000000000000000000000000000000000000-2200
χ1522222-1222222-12-1-12222-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100220000000000000200-1-100-1-12-1-10000
χ1622222-1222222-12-1-12222-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000-200110011-2110000
χ1722222-1222222-12-1-12222-12-1-1-1-122-1-1-1-1-1-1-122-2-2-1-1-1-1-1-2-2-2-211111111111100220000000000000200-1-100-1-1-2110000
χ1822222-1222222-12-1-12222-12-1-1-1-122-1-1-1-1-1-1-122-2-2-1-1-1-1-1-2-2-2-211111111111100-2-20000000000000-2001100112-1-10000
χ1922222-12-22-222-12-1-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i300220000000000000-200-1-100110−i3i30000
χ2022222-12-22-222-12-1-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i300-2-200000000000002001100-1-10i3−i30000
χ2122222-12-22-222-12-1-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i300220000000000000-200-1-100110i3−i30000
χ2222222-12-22-222-12-1-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i300-2-200000000000002001100-1-10−i3i30000
χ232222-122222-1-12-122-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122002222-1-1-1-1-1-1-1-120-1-100-1-1000000000
χ242222-122222-1-12-122-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200-2-2-2-211111111-20110011000000000
χ252222-122222-1-12-122-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1-2-22-1-1-1-11111-2-21111-2-211112200-2-2-2-21111111120-1-100-1-1000000000
χ262222-122222-1-12-122-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1-2-22-1-1-1-11111-2-21111-2-21111-2-2002222-1-1-1-1-1-1-1-1-20110011000000000
χ272222-12-22-22-1-12-1221111-1-2-1-1-1-2-1-12211-2111100-2-1-11133−3−30033−3−30033−3−3220000003333−3−3−3−3-20-1-10011000000000
χ282222-12-22-22-1-12-1221111-1-2-1-1-1-2-1-12211-2111100-2-1-11133−3−30033−3−30033−3−3-2-2000000−3−3−3−33333201100-1-1000000000
χ292222-12-22-22-1-12-1221111-1-2-1-1-1-2-1-12211-2111100-2-1-111−3−33300−3−33300−3−33322000000−3−3−3−33333-20-1-10011000000000
χ302222-12-22-22-1-12-1221111-1-2-1-1-1-2-1-12211-2111100-2-1-111−3−33300−3−33300−3−333-2-20000003333−3−3−3−3201100-1-1000000000
χ3122-2-222020-22-2-2-22-20000202-2-202-22-20000000−i2i202-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002-20000000000000
χ3222-2-222020-22-2-2-22-20000202-2-202-22-20000000−i2i202-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-2200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200-220000000000000
χ3322-2-222020-22-2-2-22-20000202-2-202-22-20000000i2−i202-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002-20000000000000
χ3422-2-222020-22-2-2-22-20000202-2-202-22-20000000i2−i202-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-2200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200-220000000000000
χ3522-2-2-12020-2-11-212-23−33−3-10-1110-112-23−303−33−3−i2i20-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ232-200−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300-11003−3000000000
χ3622-2-2-12020-2-11-212-23−33−3-10-1110-112-23−303−33−3−i2i20-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23-2200i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23001-100−33000000000
χ3722-2-2-12020-2-11-212-23−33−3-10-1110-112-23−303−33−3i2−i20-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ232-200i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300-11003−3000000000
χ3822-2-2-12020-2-11-212-23−33−3-10-1110-112-23−303−33−3i2−i20-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23-2200−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23001-100−33000000000
χ3922-2-2-12020-2-11-212-2−33−33-10-1110-112-2−330−33−33−i2i20-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ72-200−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700-1100−33000000000
χ4022-2-2-12020-2-11-212-2−33−33-10-1110-112-2−330−33−33−i2i20-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7-2200i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7001-1003−3000000000
χ4122-2-2-12020-2-11-212-2−33−33-10-1110-112-2−330−33−33i2−i20-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ72-200i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700-1100−33000000000
χ4222-2-2-12020-2-11-212-2−33−33-10-1110-112-2−330−33−33i2−i20-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7-2200−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7001-1003−3000000000
χ432-22-22220-20-2-222-2-222-2-220-22-22000022-2-2-20000000000000000000000000002-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200002-2000000000−i2i2
χ442-22-22220-20-2-222-2-222-2-220-22-22000022-2-2-20000000000000000000000000002-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200002-2000000000i2−i2
χ452-22-22220-20-2-222-2-222-2-220-22-22000022-2-2-2000000000000000000000000000-22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000-22000000000i2−i2
χ462-22-22220-20-2-222-2-222-2-220-22-22000022-2-2-2000000000000000000000000000-22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000-22000000000−i2i2
χ4744444-2-44-4444-24-2-2-4-4-4-4-2-4-2-2-2244-2-222222-4-4002-2-2220000000000000000000000000000000000000000000000000
χ4844444-2-4-4-4-444-24-2-2-4-4-4-4-24-2-2-22-4-422222224400-222-2-20000000000000000000000000000000000000000000000000
χ494444-244-44-4-2-24-244-2-2-2-2-2-4-2-2-2422-4-4-2-24-2-22200-422220000000000000000000000000000000000000000000000000
χ504444-24-4-4-4-4-2-24-2442222-24-2-2-2-422-4-422-422-2-200422-2-20000000000000000000000000000000000000000000000000
χ514444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-244-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000000000
χ524444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-2-4-4-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000000000
χ534444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-4111-2222211-21122002-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000000000000
χ544444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-4111-2222211-21122002-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000000000000
χ554444-2-2-44-44-2-2-2-2-2-222221-41112-2-2-2-2-1-12-1-12200211-1-12323−23−2300−3−33300−3−333000000000000000000000000000000000
χ564444-2-2-44-44-2-2-2-2-2-222221-41112-2-2-2-2-1-12-1-12200211-1-1−23−2323230033−3−30033−3−3000000000000000000000000000000000
χ574444-2-2-4-4-4-4-2-2-2-2-2-222221411122222-1-12-1-1-2-200-2-1-1110000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000000000
χ584444-2-2-4-4-4-4-2-2-2-2-2-222221411122222-1-12-1-1-2-200-2-1-111000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000000000
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χ6144-4-44-2040-44-42-4-220000-20-22204-4-2200000002i2−2i20-22002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000000
χ6244-4-44-20-4044-42-4-220000-20-2220-442-200000000002-20000006−66−66−6−66−66−66000000000000000000000000000000000
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χ6644-4-4-2-2040-4-2222-2223−2323−23101-1-10-22-22−330−3323−23−2i22i201-1−332ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000000000000000000000000
χ6744-4-4-2-2040-4-2222-2223−2323−23101-1-10-22-22−330−3323−232i2−2i201-1−33−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000000000000000000000000
χ6844-4-4-2-2040-4-2222-22−2323−2323101-1-10-22-223−303−3−2323−2i22i201-13−32ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000000000000000000000000
χ6944-4-4-2-2040-4-2222-22−2323−2323101-1-10-22-223−303−3−23232i2−2i201-13−3−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000000000000000000000000
χ7044-4-4-2-20-404-2222-2223−2323−23101-1-102-22-2−330−33−2323000-113−300006−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23000000000000000000000000000000000
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χ7244-4-4-2-20-404-2222-22−2323−2323101-1-102-22-23−303−323−23000-11−3300006−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−662ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23000000000000000000000000000000000
χ7344-4-4-2-20-404-2222-22−2323−2323101-1-102-22-23−303−323−23000-11−330000−662ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ236−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23000000000000000000000000000000000
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χ784-44-44-2-4040-4-4-2422-4-444-202-222000022-2-2-20000000000000000000000000000000000000000000000000−23230000000
χ794-44-4-2440-40224-2-4-4-2-222-202-2240000-2-2-42200000000000000000000000000000−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i200000000000000000
χ804-44-4-2440-40224-2-4-4-2-222-202-2240000-2-2-422000000000000000000000000000002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i200000000000000000
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χ834-4-44440000-44-4-4-44000040-4-440000000000000000000000000000000000000002-2-222-2-222-2-2200000000000000000
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χ854-4-44-2400002-2-42-4423−23−2323-2022-20000023−230−2323000000000000000000000000000002-2-22−1−31+31+3−1−3−1+31−31−3−1+300000000000000000
χ864-4-44-2400002-2-42-4423−23−2323-2022-20000023−230−232300000000000000000000000000000-222-21+3−1−3−1−31+31−3−1+3−1+31−300000000000000000
χ874-4-44-2400002-2-42-44−232323−23-2022-200000−2323023−23000000000000000000000000000002-2-22−1+31−31−3−1+3−1−31+31+3−1−300000000000000000
χ884-4-44-2400002-2-42-44−232323−23-2022-200000−2323023−2300000000000000000000000000000-222-21−3−1+3−1+31−31+3−1−3−1−31+300000000000000000
χ898-88-8-4-480-8044-4-444-4-44420-22-2-40000224-2-20000000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4-808044-4-44444-4-420-22-240000-2-2-4220000000000000000000000000000000000000000000000000000000000
χ918-8-888-40000-884-84-40000-4044-400000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88-4-400004-4444-443−43−434320-2-2200000−2323023−230000000000000000000000000000000000000000000000000000000000
χ938-8-88-4-400004-4444-4−434343−4320-2-220000023−230−23230000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.