Finite Group Databasebeta

← Group #13138992

Character table — Group #13138992

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1122222222244444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636727272727272727272727272
order122344666888121224242424336612121212242424243666661212121212122424242424242424242424242424246688121224242424246688121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111-1-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1111-1-1-111-1-1
χ6111111111-1-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11-1-1-1111-1-111
χ7111111111-1-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-111-11-1-1-1-111
χ8111111111-1-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-1-11-11111-1-1
χ92222222222222222222-12-1-1-122-1-1-1-1-12-1-1-1-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ102222222222222222222-12-1-1-122-1-1-1-1-12-1-1-1-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ11222222222222222222-12-1222-1-12222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000000002200-1-1-1-1
χ12222222222222222222-12-1222-1-12222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2001111
χ13222222222-2-2-222-2-2-2-22-12-1-1-1221111-12-1-1-1-1-1-1-12-1-111-2-2-2-21111111122-1-1-2-2-1-11111000000000000
χ14222222222-2-2-222-2-2-2-22-12-1-1-1221111-12-1-1-1-1-1-1-12-1-111-2-2-2-211111111-2-2112211-1-1-1-1000000000000
χ15222222222-2-2-222-2-2-2-2-12-1222-1-1-2-2-2-2-1-12-1-1-12-1-1-1-1-1-2-211111111111100000000000000002-200-1-111
χ16222222222-2-2-222-2-2-2-2-12-1222-1-1-2-2-2-2-1-12-1-1-12-1-1-1-1-1-2-21111111111110000000000000000-220011-1-1
χ172222-2-2222000-2-200002222-2-2-2-20000222222-2-2-2-2-2-20000000000000000002i−2i002i2i−2i−2i000000000000
χ182222-2-2222000-2-200002222-2-2-2-20000222222-2-2-2-2-2-2000000000000000000−2i2i00−2i−2i2i2i000000000000
χ192222-2-2222000-2-200002-12-111-2-233−3−3-12-1-1-1-1111-2113−300003333−3−3−3−300−i3i32i−2i−i3i3−i−iii000000000000
χ202222-2-2222000-2-200002-12-111-2-233−3−3-12-1-1-1-1111-2113−300003333−3−3−3−300i3−i3−2i2ii3−i3ii−i−i000000000000
χ212222-2-2222000-2-200002-12-111-2-2−3−333-12-1-1-1-1111-211−330000−3−3−3−3333300−i3i3−2i2i−i3i3ii−i−i000000000000
χ222222-2-2222000-2-200002-12-111-2-2−3−333-12-1-1-1-1111-211−330000−3−3−3−3333300i3−i32i−2ii3−i3−i−iii000000000000
χ2322-222-2-2-2222-2-2222-2-2222222-2-222222-2-2-2-22-2-2-2222-2-222-2-222-2-222-2-2000000000000000000000000
χ2422-222-2-2-2222-2-2222-2-22-12-1-1-1-2-2-1-1-1-1-1-2111-11112-1-11122-2-2-1-111-1-11100−i3i300i3−i3−i3i3−i3i3000000000000
χ2522-222-2-2-2222-2-2222-2-22-12-1-1-1-2-2-1-1-1-1-1-2111-11112-1-11122-2-2-1-111-1-11100i3−i300−i3i3i3−i3i3−i3000000000000
χ2622-222-2-2-2222-2-2222-2-2-12-1222112222-11-211-1-211-1-1-1-2-2-1-111-1-111-1-111000000000000000000003−33−3
χ2722-222-2-2-2222-2-2222-2-2-12-1222112222-11-211-1-211-1-1-1-2-2-1-111-1-111-1-11100000000000000000000−33−33
χ2822-222-2-2-22-2-22-22-2-222222222-2-2-2-2-2-22-2-2-2-22-2-2-222222-2-222-2-222-2-222000000000000000000000000
χ2922-222-2-2-22-2-22-22-2-2222-12-1-1-1-2-21111-1-2111-11112-1-1-1-1-2-22211-1-111-1-100−i3i300i3−i3i3−i3i3−i3000000000000
χ3022-222-2-2-22-2-22-22-2-2222-12-1-1-1-2-21111-1-2111-11112-1-1-1-1-2-22211-1-111-1-100i3−i300−i3i3−i3i3−i3i3000000000000
χ3122-222-2-2-22-2-22-22-2-222-12-122211-2-2-2-2-11-211-1-211-1-1-12211-1-111-1-111-1-1000000000000000000003−3−33
χ3222-222-2-2-22-2-22-22-2-222-12-122211-2-2-2-2-11-211-1-211-1-1-12211-1-111-1-111-1-100000000000000000000−333−3
χ3322-22-22-2-220002-200002222-2-22200002-2-2-2-22222-2-2-2000000000000002-22200-2-20000000000000000
χ3422-22-22-2-220002-200002222-2-22200002-2-2-2-22222-2-2-200000000000000-22-2-200220000000000000000
χ3522-22-22-2-220002-200002-12-1112233−3−3-1-2111-1-1-1-1-211−33000033−3−3−3−3332-2-1-100113−3−33000000000000
χ3622-22-22-2-220002-200002-12-1112233−3−3-1-2111-1-1-1-1-211−33000033−3−3−3−333-221100-1-1−333−3000000000000
χ3722-22-22-2-220002-200002-12-11122−3−333-1-2111-1-1-1-1-2113−30000−3−33333−3−32-2-1-10011−333−3000000000000
χ3822-22-22-2-220002-200002-12-11122−3−333-1-2111-1-1-1-1-2113−30000−3−33333−3−3-221100-1-13−3−33000000000000
χ39444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2111-211-211-2-2-2-2-2-211111111000000000000000000000000
χ40444444444-4-4-444-4-4-4-4-2-2-2-2-2-2-2-222221-2-2111-211-211222222-1-1-1-1-1-1-1-1000000000000000000000000
χ414444-4-4444000-4-40000-24-24-4-4220000-2-24-2-2-2-42222200000000000000000000000000000000000000
χ424444-4-4444000-4-40000-2-2-2-222222323−23−231-2-21112-1-12-1-123−230000−3−3−3−33333000000000000000000000000
χ434444-4-4444000-4-40000-2-2-2-22222−23−2323231-2-21112-1-12-1-1−232300003333−3−3−3−3000000000000000000000000
χ4444-444-4-4-4444-4-4444-4-4-2-2-2-2-2-222-2-2-2-2122-1-112-1-1-21122-2-22211-1-111-1-1000000000000000000000000
χ4544-444-4-4-44-4-44-44-4-444-2-2-2-2-2-2222222122-1-112-1-1-211-2-222-2-2-1-111-1-111000000000000000000000000
χ4644-44-44-4-440004-40000-24-24-4-4-2-20000-22-422-24-2-222200000000000000000000000000000000000000
χ4744-44-44-4-440004-40000-2-2-2-222-2-22323−23−23122-1-11-2112-1-1−23230000−3−33333−3−3000000000000000000000000
χ4844-44-44-4-440004-40000-2-2-2-222-2-2−23−232323122-1-11-2112-1-123−23000033−3−3−3−333000000000000000000000000
χ494-4040000-4−2i22i2000−2i22i20044-4-40000−2i22i2−2i22i240000-400000000−2i22i200−2i22i200−2i22i200000000000000000000000000
χ504-4040000-4−2i22i2000−2i22i2004-2-4223−23002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23-200002000023−2300−2i22i2002ζ5+2ζ7−2ζ5−2ζ7002ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000
χ514-4040000-4−2i22i2000−2i22i2004-2-42−2323002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7-2000020000−232300−2i22i2002ζ13+2ζ23−2ζ13−2ζ23002ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000
χ524-4040000-4−2i22i2000−2i22i200-242-40023−23−2i22i2−2i22i2-200002023−2300000i2−i2i6−i6i2−i2i6−i6i2−i2i6−i6000000000000000000000000
χ534-4040000-4−2i22i2000−2i22i200-242-400−2323−2i22i2−2i22i2-2000020−232300000i2−i2−i6i6i2−i2−i6i6i2−i2−i6i6000000000000000000000000
χ544-4040000-4−2i22i2000−2i22i200-2-22223−2323−232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ231003-3-10−330−3300i2−i2i6−i6−ζ5−ζ7ζ5+ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ13−ζ23ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000
χ554-4040000-4−2i22i2000−2i22i200-2-22223−23−23232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23100-33-103−30−3300i2−i2−i6i6−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ13−ζ23ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000
χ564-4040000-4−2i22i2000−2i22i200-2-222−232323−232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7100-33-10−3303−300i2−i2i6−i6−ζ13−ζ23ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000
χ574-4040000-4−2i22i2000−2i22i200-2-222−2323−23232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ71003-3-103−303−300i2−i2−i6i6−ζ13−ζ23ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000
χ584-4040000-42i2−2i20002i2−2i20044-4-400002i2−2i22i2−2i240000-4000000002i2−2i2002i2−2i2002i2−2i200000000000000000000000000
χ594-4040000-42i2−2i20002i2−2i2004-2-4223−2300−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23-200002000023−23002i2−2i200−2ζ5−2ζ72ζ5+2ζ700−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000
χ604-4040000-42i2−2i20002i2−2i2004-2-42−232300−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7-2000020000−2323002i2−2i200−2ζ13−2ζ232ζ13+2ζ2300−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000
χ614-4040000-42i2−2i20002i2−2i200-242-40023−232i2−2i22i2−2i2-200002023−2300000−i2i2−i6i6−i2i2−i6i6−i2i2−i6i6000000000000000000000000
χ624-4040000-42i2−2i20002i2−2i200-242-400−23232i2−2i22i2−2i2-2000020−232300000−i2i2i6−i6−i2i2i6−i6−i2i2i6−i6000000000000000000000000
χ634-4040000-42i2−2i20002i2−2i200-2-22223−2323−23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ231003-3-10−330−3300−i2i2−i6i6ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ13+ζ23−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000
χ644-4040000-42i2−2i20002i2−2i200-2-22223−23−2323−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23100-33-103−30−3300−i2i2i6−i6ζ5+ζ7−ζ5−ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ13+ζ23−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000
χ654-4040000-42i2−2i20002i2−2i200-2-222−232323−23−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7100-33-10−3303−300−i2i2−i6i6ζ13+ζ23−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000
χ664-4040000-42i2−2i20002i2−2i200-2-222−2323−2323−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ71003-3-103−303−300−i2i2i6−i6ζ13+ζ23−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000
χ67666-366-3-3-3666-3-3-3-3-3-30000000000000000000000000000000000000000000000000022-1-100-1-10000
χ68666-366-3-3-3666-3-3-3-3-3-300000000000000000000000000000000000000000000000000-2-21100110000
χ69666-366-3-3-3-6-6-6-3-33333000000000000000000000000000000000000000000000000002-2-1-100110000
χ70666-366-3-3-3-6-6-6-3-3333300000000000000000000000000000000000000000000000000-221100-1-10000
χ7166-6-36-633-366-63-3-3-3330000000000000000000000000000000000000000000000000000−i3i300−i3i30000
χ7266-6-36-633-366-63-3-3-3330000000000000000000000000000000000000000000000000000i3−i300i3−i30000
χ7366-6-36-633-3-6-663-333-3-30000000000000000000000000000000000000000000000000000−i3i300i3−i30000
χ7466-6-36-633-3-6-663-333-3-30000000000000000000000000000000000000000000000000000i3−i300−i3i30000
χ75121212-6-12-12-6-6-600066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-6-121266-6000-66000000000000000000000000000000000000000000000000000000000000000000
χ7712-120-600−6i36i36−6i26i20003i2−3i236−3600000000000000000000000000000000000000000000000000000000000000
χ7812-120-600−6i36i366i2−6i2000−3i23i2−363600000000000000000000000000000000000000000000000000000000000000
χ7912-120-6006i3−6i36−6i26i20003i2−3i2−363600000000000000000000000000000000000000000000000000000000000000
χ8012-120-6006i3−6i366i2−6i2000−3i23i236−3600000000000000000000000000000000000000000000000000000000000000

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