Finite Group Databasebeta

← Group #11799753

Character table — Group #11799753

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size112222222224444444444444444444888888888888888888888888181824242424363636484848484848484848487272
order1223344668836668121212121212242424242424242461216162424242448484848484848484848484848484848882488448446121212121224241616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-11-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1
χ511111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111-1-1
χ611111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1
χ711111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-111-1-111
χ811111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-111-1-11111
χ9222222222-2-22222-2222222-2-2-2-2-2-2-2-22200-2-2-2-20000000000000000220000-2-22000000000000
χ10222222222-2-22222-2222222-2-2-2-2-2-2-2-22200-2-2-2-20000000000000000-2-2000022-2000000000000
χ112222-1222-122-1-12-12-12-1-1-1222-1-1-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100220000020-1-1-1-1000000
χ122222-1222-122-1-12-12-12-1-1-1222-1-1-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200000-201111000000
χ132222-1222-122-1-12-12-12-1-1-1222-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2-2-2111111111111002200000-20-1-111000000
χ142222-1222-122-1-12-12-12-1-1-1222-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2-2-211111111111100-2-2000002011-1-1000000
χ15222-1222-1222-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000022000020000-1-1-1-100
χ16222-1222-1222-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-20000-20000111100
χ17222-1222-1222-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-2-2-12-1-11111-2-2-2-2111111110000220000-2000011-1-100
χ18222-1222-1222-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-2-2-12-1-11111-2-2-2-2111111110000-2-2000020000-1-11100
χ1922-2222-2222222-2-2-2-22222-222222222-2-200-2-2-2-2000000000000000000002i−2i000000000002i−2i00
χ2022-2222-2222222-2-2-2-22222-222222222-2-200-2-2-2-200000000000000000000−2i2i00000000000−2i2i00
χ2122-2222-222-2-222-2-22-22222-2-2-2-2-2-2-2-2-2-2-20022220000000000000000002-200000002-200000000
χ2222-2222-222-2-222-2-22-22222-2-2-2-2-2-2-2-2-2-2-2002222000000000000000000-220000000-2200000000
χ2322-222-22220022-2-202-2-2-2-2200000000-22−i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i222000000-20000000000−i2i2
χ2422-222-22220022-2-202-2-2-2-2200000000-22−i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2-2-200000020000000000i2−i2
χ2522-222-22220022-2-202-2-2-2-2200000000-22i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i222000000-20000000000i2−i2
χ2622-222-22220022-2-202-2-2-2-2200000000-22i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2-2-200000020000000000−i2i2
χ2722-22-12-22-1-2-2-1-1-21212-1-1-1-2-2-211111111002-1-1-100003−33−333−3−333−3−3002-20000000-113−3000000
χ2822-22-12-22-1-2-2-1-1-21212-1-1-1-2-2-211111111002-1-1-100003−33−333−3−333−3−300-2200000001-1−33000000
χ2922-22-12-22-1-2-2-1-1-21212-1-1-1-2-2-211111111002-1-1-10000−33−33−3−333−3−333002-20000000-11−33000000
χ3022-22-12-22-1-2-2-1-1-21212-1-1-1-2-2-211111111002-1-1-10000−33−33−3−333−3−33300-2200000001-13−3000000
χ3122-2-122-2-1222-1-11-2-2-2-12-1-11-1-122-1-1-1-111001-211−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300002i−2i0000000003−3−ii00
χ3222-2-122-2-1222-1-11-2-2-2-12-1-11-1-122-1-1-1-111001-211−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i30000−2i2i000000000−33i−i00
χ3322-2-122-2-1222-1-11-2-2-2-12-1-11-1-122-1-1-1-111001-211i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300002i−2i000000000−33−ii00
χ3422-2-122-2-1222-1-11-2-2-2-12-1-11-1-122-1-1-1-111001-211i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i30000−2i2i0000000003−3i−i00
χ3544444-4-4440044440-4-4-4-4-4-4000000004-40000000000000000000000000000000000000000000
χ364444-2444-2-4-4-2-24-2-4-24-2-2-24-4-4222222-2-200-42220000000000000000000000000000000000000
χ374444-2-4-44-200-2-24-202-4222-400000000-220000000000i6−i6−i6i6i6i6−i6−i6−i6−i6i6i6000000000000000000000
χ384444-2-4-44-200-2-24-202-4222-400000000-220000000000−i6i6i6−i6−i6−i6i6i6i6i6−i6−i6000000000000000000000
χ39444-2444-24-4-4-2-2-24-44-24-2-2-222-4-42222-2-2002-4220000000000000000000000000000000000000
χ40444-24-4-4-2400-2-2-240-42-422200000000-220000006−6−6600006−66−6−66−66000000000000000000000
χ41444-24-4-4-2400-2-2-240-42-422200000000-22000000−666−60000−66−666−66−6000000000000000000000
χ42444-2-244-2-24411-2-24-2-2-211-2-2-2-2-211111144-2-211-2-2-2-2-2-2-2-211111111000000000000000000000
χ43444-2-244-2-24411-2-24-2-2-211-2-2-2-2-2111111-4-4-2-21122222222-1-1-1-1-1-1-1-1000000000000000000000
χ44444-2-244-2-2-4-411-2-2-4-2-2-211-22222-1-1-1-1110022-1-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000
χ45444-2-244-2-2-4-411-2-2-4-2-2-211-22222-1-1-1-1110022-1-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000
χ46444-2-2-4-4-2-20011-2-20222-1-1200003i3i−3i−3i1-100003i−3i6−6−66i6−i6−i6i6−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13000000000000000000000
χ47444-2-2-4-4-2-20011-2-20222-1-1200003i3i−3i−3i1-100003i−3i−666−6−i6i6i6−i6ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13000000000000000000000
χ48444-2-2-4-4-2-20011-2-20222-1-120000−3i−3i3i3i1-10000−3i3i6−6−66−i6i6i6−i6ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23000000000000000000000
χ49444-2-2-4-4-2-20011-2-20222-1-120000−3i−3i3i3i1-10000−3i3i−666−6i6−i6−i6i6−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23000000000000000000000
χ5044-44-24-44-244-2-2-42-424-2-2-2-444-2-2-2-2-2-22200-42220000000000000000000000000000000000000
χ5144-44-2-444-200-2-2-420-2-42224000000002-2−2i22i20000−2i2−2i22i22i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000000000000000000
χ5244-44-2-444-200-2-2-420-2-42224000000002-22i2−2i200002i22i2−2i2−2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2000000000000000000000
χ5344-4-244-4-24-4-4-2-22-44-4-24-2-2222-4-422222200-24-2-20000000000000000000000000000000000000
χ5444-4-24-44-2400-2-22-4042-422-2000000002-2−2i22i20000i2i2−i2−i2−2i2−2i22i22i2i2i2i2i2−i2−i2−i2−i2000000000000000000000
χ5544-4-24-44-2400-2-22-4042-422-2000000002-22i2−2i20000−i2−i2i2i22i22i2−2i2−2i2−i2−i2−i2−i2i2i2i2i2000000000000000000000
χ5644-4-2-24-4-2-2441122-42-2-2112-2-2-2-21111-1-10022-1-1−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i3000000000000000000000
χ5744-4-2-24-4-2-2441122-42-2-2112-2-2-2-21111-1-10022-1-12i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i3000000000000000000000
χ5844-4-2-24-4-2-2-4-4112242-2-21122222-1-1-1-1-1-100-2-211000023−2323−23−3−333−3−333000000000000000000000
χ5944-4-2-24-4-2-2-4-4112242-2-21122222-1-1-1-1-1-100-2-2110000−2323−232333−3−333−3−3000000000000000000000
χ6044-4-2-2-44-2-20011220-222-1-1-200003i3i−3i−3i-11−2i22i200−3i3ii2i2−i2−i2i2i2−i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23000000000000000000000
χ6144-4-2-2-44-2-20011220-222-1-1-200003i3i−3i−3i-112i2−2i200−3i3i−i2−i2i2i2−i2−i2i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23000000000000000000000
χ6244-4-2-2-44-2-20011220-222-1-1-20000−3i−3i3i3i-11−2i22i2003i−3ii2i2−i2−i2i2i2−i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23000000000000000000000
χ6344-4-2-2-44-2-20011220-222-1-1-20000−3i−3i3i3i-112i2−2i2003i−3i−i2−i2i2i2−i2−i2i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23000000000000000000000
χ644-404400-4-4−2i22i24-4000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000022−2200002i−2i0000000000000
χ654-404400-4-4−2i22i24-4000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000−22220000−2i2i0000000000000
χ664-404400-4-42i2−2i24-40000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000022−220000−2i2i0000000000000
χ674-404400-4-42i2−2i24-40000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000−222200002i−2i0000000000000
χ688-808-400-84−4i24i2-44000000000−4i24i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ698-808-400-844i2−4i2-440000000004i2−4i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000000000
χ708-80-48004-8−4i24i2-440000000002i2−2i2−4i24i22i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ718-80-48004-84i2−4i2-44000000000−2i22i24i2−4i2−2i22i2−2i22i2000000000000000000000000000000000000000000000
χ728-80-4-40044−4i24i22-20000006i−6i02i2−2i22i2−2i2−4ζ5+2ζ7−4ζ13+2ζ234ζ5−2ζ7+4ζ13−2ζ232ζ5−4ζ7+2ζ13−4ζ23−2ζ5+4ζ7−2ζ13+4ζ23000000000000000000000000000000000000000000000
χ738-80-4-40044−4i24i22-2000000−6i6i02i2−2i22i2−2i22ζ5−4ζ7+2ζ13−4ζ23−2ζ5+4ζ7−2ζ13+4ζ23−4ζ5+2ζ7−4ζ13+2ζ234ζ5−2ζ7+4ζ13−2ζ23000000000000000000000000000000000000000000000
χ748-80-4-400444i2−4i22-20000006i−6i0−2i22i2−2i22i24ζ5−2ζ7+4ζ13−2ζ23−4ζ5+2ζ7−4ζ13+2ζ23−2ζ5+4ζ7−2ζ13+4ζ232ζ5−4ζ7+2ζ13−4ζ23000000000000000000000000000000000000000000000
χ758-80-4-400444i2−4i22-2000000−6i6i0−2i22i2−2i22i2−2ζ5+4ζ7−2ζ13+4ζ232ζ5−4ζ7+2ζ13−4ζ234ζ5−2ζ7+4ζ13−2ζ23−4ζ5+2ζ7−4ζ13+2ζ23000000000000000000000000000000000000000000000

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