Finite Group Databasebeta

← Group #11781633

Character table — Group #11781633

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222222244444444444444444888888888888888888888888242424242424242424242424363636364848484848487272
order122233444466666634666121212121212121212121212881212121212122424242424242424242424242424242424668812122424242488882466121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-11-1-11111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-111
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ92222222-2-222222222-222222-2-2-2222222-200-2-2-2-2-2-200000000000000002-22200-2-20000000000000000
χ102222222-2-222222222-222222-2-2-2222222-200-2-2-2-2-2-20000000000000000-22-2-200220000000000000000
χ11222222-222-22222222-2222-2-2222-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000022-2-200000000
χ12222222-222-22222222-2222-2-2222-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000-2-22200000000
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000002i−2i002i2i−2i−2i000000000000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-22200000000000000000000−2i2i00−2i−2i2i2i000000000000
χ1522222-1222222-1-1-12-12-1-1-12-1-1-12-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-100-1-10000000020-1-10000
χ1622222-1222222-1-1-12-12-1-1-12-1-1-12-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211001100000000-20110000
χ1722222-1222222-1-1-12-12-1-1-12-1-1-12-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-211111111111122-1-100-1-100000000-20110000
χ1822222-1222222-1-1-12-12-1-1-12-1-1-12-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-2111111111111-2-21100110000000020-1-10000
χ1922222-12-2-2222-1-1-12-1-2-1-1-12-111-2-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i32-2-1-100110000000000−i3i30000
χ2022222-12-2-2222-1-1-12-1-2-1-1-12-111-2-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-221100-1-10000000000i3−i30000
χ2122222-12-2-2222-1-1-12-1-2-1-1-12-111-2-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i32-2-1-100110000000000i3−i30000
χ2222222-12-2-2222-1-1-12-1-2-1-1-12-111-2-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-221100-1-10000000000−i3i30000
χ232222-122222-1-1222-1-12-1-1-1-1222-1-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100002200-1-1-1-100000200-1-100
χ242222-122222-1-1222-1-12-1-1-1-1222-1-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-200111100000-2001100
χ252222-122222-1-1222-1-12-1-1-1-1222-1-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-2111100002200-1-1-1-100000-2001100
χ262222-122222-1-1222-1-12-1-1-1-1222-1-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-211110000-2-200111100000200-1-100
χ272222-12-2-2-2-2-1-1222-1-12-1-1-11-2-2-21111-211100-1211-1-133−3−30033−3−30033−3−300002i−2i00−i−iii00000000−i3i300
χ282222-12-2-2-2-2-1-1222-1-12-1-1-11-2-2-21111-211100-1211-1-133−3−30033−3−30033−3−30000−2i2i00ii−i−i00000000i3−i300
χ292222-12-2-2-2-2-1-1222-1-12-1-1-11-2-2-21111-211100-1211-1-1−3−33300−3−33300−3−33300002i−2i00−i−iii00000000i3−i300
χ302222-12-2-2-2-2-1-1222-1-12-1-1-11-2-2-21111-211100-1211-1-1−3−33300−3−33300−3−3330000−2i2i00ii−i−i00000000−i3i300
χ312-2-22220-220-2-2-2-222202-2-2002-2-200000022−2002-2002−22−22−22−22−22−22−22−2000000000000002-20000002−2
χ322-2-22220-220-2-2-2-222202-2-2002-2-200000022−2002-2002−22−22−22−22−22−22−22−200000000000000-22000000−22
χ332-2-22220-220-2-2-2-222202-2-2002-2-20000002−22002-200−22−22−22−22−22−22−22−22000000000000002-2000000−22
χ342-2-22220-220-2-2-2-222202-2-2002-2-20000002−22002-200−22−22−22−22−22−22−22−2200000000000000-220000002−2
χ3544444-2-444-444-2-2-24-2-4-2-2-2-42-2-2422-4222400-42-2-2220000000000000000000000000000000000000000
χ3644444-2-4-4-4-444-2-2-24-24-2-2-2-4222-422-4222-4004-222-2-20000000000000000000000000000000000000000
χ374444-244-4-44-2-2444-2-2-4-2-2-2-24-4-42-2-2-24-2-22002-422220000000000000000000000000000000000000000
χ384444-24-444-4-2-2444-2-2-4-2-2-22-444-2222-422-2002-4-2-2220000000000000000000000000000000000000000
χ394444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-244-2-21111-2-2-2-2-2-21111-2-21111000000000000000000000000
χ404444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-2-4-4-2-21111222222-1-1-1-122-1-1-1-1000000000000000000000000
χ414444-2-24-4-44-2-2-2-2-2-21-4111-2-222211-2-21120022-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000
χ424444-2-24-4-44-2-2-2-2-2-21-4111-2-222211-2-21120022-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000
χ434444-2-2-444-4-2-2-2-2-2-21-411122-2-2-2-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000
χ444444-2-2-444-4-2-2-2-2-2-21-411122-2-2-2-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000
χ454444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1112323−23−2300−3−33300−3−333000000000000000000000000
χ464444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-111−23−2323230033−3−30033−3−3000000000000000000000000
χ4744-4-44400004-44-4-4-440-44-4000000000000000000000000000000000000000000000000−2i22i20000000000
χ4844-4-44400004-44-4-4-440-44-40000000000000000000000000000000000000000000000002i2−2i20000000000
χ494-44-444400-4-44-44-4-440-4-444400044-4-4-4-40000000000000000000000000000000000000000000000000
χ504-44-444-4004-44-44-4-440-4-44-4-4000-4-444440000000000000000000000000000000000000000000000000
χ514-44-44-2400-4-442-22-4-2022-24-2000-2-2-4222000000000000000000000000000000023−230000000000000000
χ524-44-44-2400-4-442-22-4-2022-24-2000-2-2-42220000000000000000000000000000000−23230000000000000000
χ534-44-44-2-4004-442-22-4-2022-2-42000224-2-2-2000000000000000000000000000−2i32i300000000000000000000
χ544-44-44-2-4004-442-22-4-2022-2-42000224-2-2-20000000000000000000000000002i3−2i300000000000000000000
χ554-44-4-24400-42-2-44-42-2022-2-24000-2-22-422000000000000000000000000000000000i6−i6i6−i6000000000000
χ564-44-4-24400-42-2-44-42-2022-2-24000-2-22-422000000000000000000000000000000000−i6i6−i6i6000000000000
χ574-44-4-24-40042-2-44-42-2022-22-400022-24-2-20000000000000000000000000000000006−6−66000000000000
χ584-44-4-24-40042-2-44-42-2022-22-400022-24-2-2000000000000000000000000000000000−666−6000000000000
χ594-4-444404-40-4-4-4-444404-4-400-444000000-40000-44000000000000000000000000000000000000000000
χ604-4-444-204-40-4-422-24-20-222002-24000000-400002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000
χ614-4-444-204-40-4-422-24-20-222002-24000000-400002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000
χ624-4-444-20-440-4-422-24-20-22200-22-4000000422−2200-220022−2222−22−22−22−22−22−22−22000000000000000000000000
χ634-4-444-20-440-4-422-24-20-22200-22-40000004−222200-2200−2222−22222−22−22−22−22−22−2000000000000000000000000
χ644-4-44-2404-4022-4-44-2-20-22200-44-2000000200002-2006−6−66006−6−66006−6−66000000000000000000000000
χ654-4-44-2404-4022-4-44-2-20-22200-44-2000000200002-200−666−600−666−600−666−6000000000000000000000000
χ664-4-44-240-44022-4-44-2-20-222004-42000000-222−2200-2200−22−2222−22−22−2222−22−22−22000000000000000000000000
χ674-4-44-240-44022-4-44-2-20-222004-42000000-2−222200-22002−22−2−22222−22−2−22222−22−2000000000000000000000000
χ684-4-44-2-204-402222-2-2101-1-1002-2-23i−3i003i−3i20000-113i−3i6−6−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ694-4-44-2-204-402222-2-2101-1-1002-2-23i−3i003i−3i20000-113i−3i−666−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ704-4-44-2-204-402222-2-2101-1-1002-2-2−3i3i00−3i3i20000-11−3i3i6−6−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ714-4-44-2-204-402222-2-2101-1-1002-2-2−3i3i00−3i3i20000-11−3i3i−666−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ724-4-44-2-20-4402222-2-2101-1-100-2223i−3i003i−3i-222−22001-1−3i3i−22−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23000000000000000000000000
χ734-4-44-2-20-4402222-2-2101-1-100-2223i−3i003i−3i-2−2222001-1−3i3i2−22−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23000000000000000000000000
χ744-4-44-2-20-4402222-2-2101-1-100-222−3i3i00−3i3i-222−22001-13i−3i−22−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23000000000000000000000000
χ754-4-44-2-20-4402222-2-2101-1-100-222−3i3i00−3i3i-2−2222001-13i−3i2−22−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23000000000000000000000000
χ7688-8-88-400008-8-444-8-404-44000000000000000000000000000000000000000000000000000000000000
χ7788-8-8-480000-448-8-84-404-44000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-4-40000-44-444420-22-2000006i−6i00−6i6i0000000000000000000000000000000000000000000000000
χ7988-8-8-4-40000-44-444420-22-200000−6i6i006i−6i0000000000000000000000000000000000000000000000000
χ808-88-8-4-4800-84-44-44420-2-22-4-40002244-2-20000000000000000000000000000000000000000000000000
χ818-88-8-4-4-80084-44-44420-2-2244000-2-2-4-4220000000000000000000000000000000000000000000000000

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