Finite Group Databasebeta

← Group #11799117

Character table — Group #11799117

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size112222222224444444444444444444888888888888888888888888181824242424363636484848484848484848487272
order122334466883666812121212121224242424242424246121616242424244848484848484848484848484848484888248844822666661224241616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-11-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-111-1-1
χ511111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1111-1-1
χ611111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-1-1-1-1
χ711111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-1-111
χ811111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-111-11111
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
χ112222-1222-122-12-1-12-12-1-1-1222-1-1-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022000002000-1-1-1-10000
χ122222-1222-122-12-1-12-12-1-1-1222-1-1-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200000-200011110000
χ132222-1222-122-12-1-12-12-1-1-1222-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2-2-2111111111111002200000-2000-111-10000
χ142222-1222-122-12-1-12-12-1-1-1222-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2-2-211111111111100-2-20000020001-1-110000
χ15222-1222-1222-1-12-122-12-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-100002200002-1-10000-1-100
χ16222-1222-1222-1-12-122-12-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-20000-21100001100
χ17222-1222-1222-1-12-122-12-1-1-1-1-122-1-1-1-1-1-1-2-2-12-1-11111-2-2-2-2111111110000220000-2110000-1-100
χ18222-1222-1222-1-12-122-12-1-1-1-1-122-1-1-1-1-1-1-2-2-12-1-11111-2-2-2-2111111110000-2-200002-1-100001100
χ1922-2222-222222-2-22-2-22222-222222222-2-200-2-2-2-20000000000000000002-2000000000200-20000
χ2022-2222-222222-2-22-2-22222-222222222-2-200-2-2-2-2000000000000000000-22000000000-20020000
χ2122-2222-222-2-22-2-222-22222-2-2-2-2-2-2-2-2-2-2-2002222000000000000000000002i−2i000000000002i−2i00
χ2222-2222-222-2-22-2-222-22222-2-2-2-2-2-2-2-2-2-2-200222200000000000000000000−2i2i00000000000−2i2i00
χ2322-222-2222002-2-2202-2-2-2-2200000000-222−2000022−2−222−2−22222−2−2−2−222000000-200000000002−2
χ2422-222-2222002-2-2202-2-2-2-2200000000-222−2000022−2−222−2−22222−2−2−2−2-2-200000020000000000−22
χ2522-222-2222002-2-2202-2-2-2-2200000000-22−220000−2−222−2−222−2−2−2−2222222000000-20000000000−22
χ2622-222-2222002-2-2202-2-2-2-2200000000-22−220000−2−222−2−222−2−2−2−22222-2-2000000200000000002−2
χ2722-22-12-22-122-1-21-1-212-1-1-1-222-1-1-1-1-1-11100-21110000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3002-2000000000-1−i3i310000
χ2822-22-12-22-122-1-21-1-212-1-1-1-222-1-1-1-1-1-11100-21110000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i300-220000000001i3−i3-10000
χ2922-22-12-22-122-1-21-1-212-1-1-1-222-1-1-1-1-1-11100-21110000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3002-2000000000-1i3−i310000
χ3022-22-12-22-122-1-21-1-212-1-1-1-222-1-1-1-1-1-11100-21110000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i300-220000000001−i3i3-10000
χ3122-2-122-2-12-2-2-11-2-12-2-12-1-1111-2-211111100-12-1-13−33−300003−33−33−33−300002i−2i00000−i3i30000−ii00
χ3222-2-122-2-12-2-2-11-2-12-2-12-1-1111-2-211111100-12-1-13−33−300003−33−33−33−30000−2i2i00000i3−i30000i−i00
χ3322-2-122-2-12-2-2-11-2-12-2-12-1-1111-2-211111100-12-1-1−33−330000−33−33−33−3300002i−2i00000i3−i30000−ii00
χ3422-2-122-2-12-2-2-11-2-12-2-12-1-1111-2-211111100-12-1-1−33−330000−33−33−33−330000−2i2i00000−i3i30000i−i00
χ3544444-4-4440044440-4-4-4-4-4-4000000004-40000000000000000000000000000000000000000000
χ364444-2444-2-4-4-24-2-2-4-24-2-2-24-4-4222222-2-200-42220000000000000000000000000000000000000
χ374444-2-4-44-200-24-2-202-4222-400000000-220000000000i6−i6−i6i6i6i6−i6−i6−i6−i6i6i6000000000000000000000
χ384444-2-4-44-200-24-2-202-4222-400000000-220000000000−i6i6i6−i6−i6−i6i6i6i6i6−i6−i6000000000000000000000
χ39444-2444-24-4-4-2-24-2-44-24-2-2-222-4-42222-2-2002-4220000000000000000000000000000000000000
χ40444-24-4-4-2400-2-24-20-42-422200000000-220000006−6−6600006−66−6−66−66000000000000000000000
χ41444-24-4-4-2400-2-24-20-42-422200000000-22000000−666−60000−66−666−66−6000000000000000000000
χ42444-2-244-2-2441-2-214-2-2-211-2-2-2-2-211111144-2-211-2-2-2-2-2-2-2-211111111000000000000000000000
χ43444-2-244-2-2441-2-214-2-2-211-2-2-2-2-2111111-4-4-2-21122222222-1-1-1-1-1-1-1-1000000000000000000000
χ44444-2-244-2-2-4-41-2-21-4-2-2-211-22222-1-1-1-1110022-1-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000
χ45444-2-244-2-2-4-41-2-21-4-2-2-211-22222-1-1-1-1110022-1-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000
χ46444-2-2-4-4-2-2001-2-210222-1-1200003i3i−3i−3i1-100003i−3i6−6−66i6−i6−i6i6−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13000000000000000000000
χ47444-2-2-4-4-2-2001-2-210222-1-1200003i3i−3i−3i1-100003i−3i−666−6−i6i6i6−i6ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13000000000000000000000
χ48444-2-2-4-4-2-2001-2-210222-1-120000−3i−3i3i3i1-10000−3i3i6−6−66−i6i6i6−i6ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23000000000000000000000
χ49444-2-2-4-4-2-2001-2-210222-1-120000−3i−3i3i3i1-10000−3i3i−666−6i6−i6−i6i6−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23000000000000000000000
χ5044-44-24-44-2-4-4-2-42-2424-2-2-2-4-4-422222222004-2-2-20000000000000000000000000000000000000
χ5144-44-2-444-200-2-42-20-2-42224000000002-222−2200002222−22−22−2−222−2−2−2−22222000000000000000000000
χ5244-44-2-444-200-2-42-20-2-42224000000002-2−22220000−22−22222222−2−22222−2−2−2−2000000000000000000000
χ5344-4-244-4-2444-22-4-2-4-4-24-2-22-2-244-2-2-2-222002-4220000000000000000000000000000000000000
χ5444-4-24-44-2400-22-4-2042-422-2000000002-222−220000−2−2222222−22−22−2−2−2−22222000000000000000000000
χ5544-4-24-44-2400-22-4-2042-422-2000000002-2−2222000022−2−2−22−2222222222−2−2−2−2000000000000000000000
χ5644-4-2-24-4-2-2441221-42-2-2112-2-2-2-21111-1-10022-1-10000−2i32i3−2i32i3i3i3−i3−i3i3i3−i3−i3000000000000000000000
χ5744-4-2-24-4-2-2441221-42-2-2112-2-2-2-21111-1-10022-1-100002i3−2i32i3−2i3−i3−i3i3i3−i3−i3i3i3000000000000000000000
χ5844-4-2-24-4-2-2-4-4122142-2-21122222-1-1-1-1-1-100-2-21123−2323−230000−33−33−33−33000000000000000000000
χ5944-4-2-24-4-2-2-4-4122142-2-21122222-1-1-1-1-1-100-2-211−2323−232300003−33−33−33−3000000000000000000000
χ6044-4-2-2-44-2-20012210-222-1-1-200003i3i−3i−3i-1122−2200−3i3i−2−222−2−222ζ5+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
χ6144-4-2-2-44-2-20012210-222-1-1-200003i3i−3i−3i-11−222200−3i3i22−2−222−2−2−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
χ6244-4-2-2-44-2-20012210-222-1-1-20000−3i−3i3i3i-1122−22003i−3i−2−222−2−222−2ζ5−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
χ6344-4-2-2-44-2-20012210-222-1-1-20000−3i−3i3i3i-11−2222003i−3i22−2−222−2−22ζ5+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
χ644-404400-4-422−22400-4000000022−2222−2222−2222−2200000000000000000000000022−2200002-20000000000000
χ654-404400-4-422−22400-4000000022−2222−2222−2222−22000000000000000000000000−22220000-220000000000000
χ664-404400-4-4−2222400-40000000−2222−2222−2222−222200000000000000000000000022−220000-220000000000000
χ674-404400-4-4−2222400-40000000−2222−2222−2222−2222000000000000000000000000−222200002-20000000000000
χ688-808-400-8442−42-4004000000042−42−2222−2222−2222000000000000000000000000000000000000000000000
χ698-808-400-84−4242-40040000000−424222−2222−2222−22000000000000000000000000000000000000000000000
χ708-80-48004-842−42-40040000000−222242−42−2222−2222000000000000000000000000000000000000000000000
χ718-80-48004-8−4242-4004000000022−22−424222−2222−22000000000000000000000000000000000000000000000
χ728-80-4-4004442−42200-200006i−6i0−2222−2222−4ζ5−2ζ7−4ζ13−2ζ234ζ5+2ζ7+4ζ13+2ζ232ζ5+4ζ7+2ζ13+4ζ23−2ζ5−4ζ7−2ζ13−4ζ23000000000000000000000000000000000000000000000
χ738-80-4-4004442−42200-20000−6i6i0−2222−22222ζ5+4ζ7+2ζ13+4ζ23−2ζ5−4ζ7−2ζ13−4ζ23−4ζ5−2ζ7−4ζ13−2ζ234ζ5+2ζ7+4ζ13+2ζ23000000000000000000000000000000000000000000000
χ748-80-4-40044−4242200-200006i−6i022−2222−224ζ5+2ζ7+4ζ13+2ζ23−4ζ5−2ζ7−4ζ13−2ζ23−2ζ5−4ζ7−2ζ13−4ζ232ζ5+4ζ7+2ζ13+4ζ23000000000000000000000000000000000000000000000
χ758-80-4-40044−4242200-20000−6i6i022−2222−22−2ζ5−4ζ7−2ζ13−4ζ232ζ5+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.