Finite Group Databasebeta

← Group #11771964

Character table — Group #11771964

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111224444444444444444448888888824242424242424242424242424242424242424242424242436367272727272
order12222233446666666666121212126612121212121244448888121212121212121224242424242424244448888
χ1111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ511111111-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-11ii−i−i
χ611111111-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-11−i−iii
χ711111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-11−i−iii
χ811111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-11ii−i−i
χ922222222222222222222222222222222000000000000000000000000-2-2-20000
χ1022222222-2-22222222222-2-2-2-222-2-2-2-2-2-200000000000000000000000022-20000
χ112-22-22-222002222-2-2-2-2-2-200002-200000000002−22−20000000022−2−222−2−22-200000
χ122-22-22-222002222-2-2-2-2-2-200002-20000000000−i2i2i2−i200000000−i2−i2i2i2i2i2−i2−i2-2200000
χ132-22-22-222002222-2-2-2-2-2-200002-20000000000i2−i2−i2i200000000i2i2−i2−i2−i2−i2i2i2-2200000
χ142-22-22-222002222-2-2-2-2-2-200002-20000000000−22−2200000000−2−222−2−2222-200000
χ152-22-2-22222i−2i22-2-22-2-2-22-22i2i−2i−2i-222i2i2i−2i−2i−2i0000000000000000000000000001−i−1+i1+i−1−i
χ162-22-2-22222i−2i22-2-22-2-2-22-22i2i−2i−2i-222i2i2i−2i−2i−2i000000000000000000000000000−1+i1−i−1−i1+i
χ172-22-2-2222−2i2i22-2-22-2-2-22-2−2i−2i2i2i-22−2i−2i−2i2i2i2i0000000000000000000000000001+i−1−i1−i−1+i
χ182-22-2-2222−2i2i22-2-22-2-2-22-2−2i−2i2i2i-22−2i−2i−2i2i2i2i000000000000000000000000000−1−i1+i−1+i1−i
χ194444441-2441-2111-21-211-2-2-2-2-2-211-211-222220000-1-1-1-1-1-1-1-1000000000000000
χ204444441-2441-2111-21-211-2-2-2-2-2-211-211-2-2-2-2-2000011111111000000000000000
χ214444441-2-4-41-2111-21-2112222-2-2-1-12-1-1222-2-20000-1-1-1-11111000000000000000
χ224444441-2-4-41-2111-21-2112222-2-2-1-12-1-12-2-22200001111-1-1-1-1000000000000000
χ23444444-2144-21-2-2-21-21-2-2111111-2-21-2-210000222200000000-1-1-1-1-1-1-1-10000000
χ24444444-2144-21-2-2-21-21-2-2111111-2-21-2-210000-2-2-2-200000000111111110000000
χ25444444-21-4-4-21-2-2-21-21-2-2-1-1-1-11122-122-100002i2i−2i−2i00000000−i−i−i−iiiii0000000
χ26444444-21-4-4-21-2-2-21-21-2-2-1-1-1-11122-122-10000−2i−2i2i2i00000000iiii−i−i−i−i0000000
χ274444-4-4440044-4-4-4444-440000-4-40000000000000000000000000000000000000
χ284444-4-4-2100-212221-212-23333-1-100-300-300000000000000003−33−33−33−30000000
χ294444-4-4-2100-212221-212-23333-1-100-300-30000000000000000−33−33−33−330000000
χ304444-4-4-2100-212221-212-2-3-3-3-3-1-10030030000000000000000−i3i3−i3i3i3−i3i3−i30000000
χ314444-4-4-2100-212221-212-2-3-3-3-3-1-10030030000000000000000i3−i3i3−i3−i3i3−i3i30000000
χ3244-4-4001-200-123-3-3-2-123123−2323−23003−303−30002i−2i0000−i3−i3i3i3ii−i−i000000000000000
χ3344-4-4001-200-123-3-3-2-123123−2323−23003−303−3000−2i2i0000i3i3−i3−i3−i−iii000000000000000
χ3444-4-4001-200-123-3-3-2-1231−2323−232300−330−330002i−2i0000i3i3−i3−i3ii−i−i000000000000000
χ3544-4-4001-200-123-3-3-2-1231−2323−232300−330−33000−2i2i0000−i3−i3i3i3−i−iii000000000000000
χ3644-4-4004400-4-40004-4-404000000000000002i−2i00000000−2i−2i2i2i000000000000000
χ3744-4-4004400-4-40004-4-40400000000000000−2i2i000000002i2i−2i−2i000000000000000
χ384-44-44-4-2100-21-2-22-12-1223i3i−3i−3i1-100−3i003i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ230000000
χ394-44-44-4-2100-21-2-22-12-1223i3i−3i−3i1-100−3i003i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ230000000
χ404-44-44-4-2100-21-2-22-12-122−3i−3i3i3i1-1003i00−3i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ130000000
χ414-44-44-4-2100-21-2-22-12-122−3i−3i3i3i1-1003i00−3i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ130000000
χ424-44-4-441-24i−4i1-2-1-112-121-1−2i−2i2i2i2-2ii−2i−i−i2i000000003−33−3−i3i3−i3i3000000000000000
χ434-44-4-441-24i−4i1-2-1-112-121-1−2i−2i2i2i2-2ii−2i−i−i2i00000000−33−33i3−i3i3−i3000000000000000
χ444-44-4-441-2−4i4i1-2-1-112-121-12i2i−2i−2i2-2−i−i2iii−2i000000003−33−3i3−i3i3−i3000000000000000
χ454-44-4-441-2−4i4i1-2-1-112-121-12i2i−2i−2i2-2−i−i2iii−2i00000000−33−33−i3i3−i3i3000000000000000
χ464-44-4-44-214i−4i-2122-2-12-1-22ii−i−i-11−2i−2ii2i2i−i0000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000
χ474-44-4-44-214i−4i-2122-2-12-1-22ii−i−i-11−2i−2ii2i2i−i0000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000
χ484-44-4-44-21−4i4i-2122-2-12-1-22−i−iii-112i2i−i−2i−2ii0000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000
χ494-44-4-44-21−4i4i-2122-2-12-1-22−i−iii-112i2i−i−2i−2ii0000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000
χ504-4-44001-200-12-33-321-23-1−2i32i32i3−2i300−i3i30i3−i302i−2i000000i−i−ii−333−3000000000000000
χ514-4-44001-200-12-33-321-23-1−2i32i32i3−2i300−i3i30i3−i30−2i2i000000−iii−i3−3−33000000000000000
χ524-4-44001-200-12-33-321-23-12i3−2i3−2i32i300i3−i30−i3i302i−2i000000i−i−ii3−3−33000000000000000
χ534-4-44001-200-12-33-321-23-12i3−2i3−2i32i300i3−i30−i3i30−2i2i000000−iii−i−333−3000000000000000
χ544-4-44004400-4-4000-4440-40000000000002i−2i000000−2i2i2i−2i0000000000000000000
χ554-4-44004400-4-4000-4440-4000000000000−2i2i0000002i−2i−2i2i0000000000000000000
χ568888-8-82-4002-4-2-2-2-42-4-220000440000000000000000000000000000000000000
χ5788-8-8002-400-24-666-4-24-620000000000000000000000000000000000000000000
χ5888-8-800-42004-200024-20-423−2323−2300−23230−232300000000000000000000000000000000
χ5988-8-800-42004-200024-20-4−2323−23230023−23023−2300000000000000000000000000000000
χ608-88-88-82-4002-422-24-24-2-20000-440000000000000000000000000000000000000
χ618-8-88002-400-246-6642-4-6-20000000000000000000000000000000000000000000
χ628-8-8800-42004-2000-2-4204−2i32i32i3−2i3002i3−2i30−2i32i300000000000000000000000000000000
χ638-8-8800-42004-2000-2-42042i3−2i3−2i32i300−2i32i302i3−2i300000000000000000000000000000000

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