Finite Group Databasebeta

← Group #11771828

Character table — Group #11771828

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111224444444444444444448888888824242424242424242424242424242424242424242424242436367272727272
order1222223344666666666612121212661212121212122244666688881212121224242424242424244448888
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111111-1-1-1-1
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
χ511111111-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i-1-11ii−i−i
χ611111111-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-11111−i−iii-1-1-1-1−i−i−i−iiiii-1-11−i−iii
χ711111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i-1-11−i−iii
χ811111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1−i−iii1111−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
χ112-22-22-2222i−2i2-2222-2-2-2-2-22i2i−2i−2i2-22i2i2i−2i−2i−2i0000000000000000000000000001+i−1−i1−i−1+i
χ122-22-22-2222i−2i2-2222-2-2-2-2-22i2i−2i−2i2-22i2i2i−2i−2i−2i000000000000000000000000000−1−i1+i−1+i1−i
χ132-22-22-222−2i2i2-2222-2-2-2-2-2−2i−2i2i2i2-2−2i−2i−2i2i2i2i0000000000000000000000000001−i−1+i1+i−1−i
χ142-22-22-222−2i2i2-2222-2-2-2-2-2−2i−2i2i2i2-2−2i−2i−2i2i2i2i000000000000000000000000000−1+i1−i−1−i1+i
χ152-22-2-2222002-22-2-22-2-2-220000-22000000000000002−22−2000022−2−222−2−2-2200000
χ162-22-2-2222002-22-2-22-2-2-220000-2200000000000000−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i22-200000
χ172-22-2-2222002-22-2-22-2-2-220000-2200000000000000i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i22-200000
χ182-22-2-2222002-22-2-22-2-2-220000-2200000000000000−22−220000−2−222−2−222-2200000
χ194444441-24411-2-2-2-2-21-2-21111111-2-21-2-20000000022220000-1-1-1-1-1-1-1-10000000
χ204444441-24411-2-2-2-2-21-2-21111111-2-21-2-200000000-2-2-2-20000111111110000000
χ214444441-2-4-411-2-2-2-2-21-2-2-1-1-1-111-122-122000000002i2i−2i−2i0000−i−i−i−iiiii0000000
χ224444441-2-4-411-2-2-2-2-21-2-2-1-1-1-111-122-12200000000−2i−2i2i2i0000iiii−i−i−i−i0000000
χ23444444-2144-2-211111-211-2-2-2-2-2-2-211-2112222-1-1-1-10000-1-1-1-1000000000000000
χ24444444-2144-2-211111-211-2-2-2-2-2-2-211-211-2-2-2-2111100001111000000000000000
χ25444444-21-4-4-2-211111-2112222-2-22-1-12-1-122-2-2-1-1-1-100001111000000000000000
χ26444444-21-4-4-2-211111-2112222-2-22-1-12-1-1-2-22211110000-1-1-1-1000000000000000
χ274444-4-41-20011-2222-21-223333-1-1-300-30000000000000000003−33−33−33−30000000
χ284444-4-41-20011-2222-21-223333-1-1-300-3000000000000000000−33−33−33−330000000
χ294444-4-41-20011-2222-21-22-3-3-3-3-1-13003000000000000000000−i3i3−i3i3i3−i3i3−i30000000
χ304444-4-41-20011-2222-21-22-3-3-3-3-1-13003000000000000000000i3−i3i3−i3−i3i3−i3i30000000
χ314444-4-44400444-4-4-4444-40000-4-40000000000000000000000000000000000000
χ3244-4-4004400-44-40004-4-40000000000000002i−2i000000002i2i−2i−2i000000000000000
χ3344-4-4004400-44-40004-4-4000000000000000−2i2i00000000−2i−2i2i2i000000000000000
χ3444-4-400-21002-2-13-3-312-1323−2323−230003−303−3002i−2i−i3−i3i3i30000−i−iii000000000000000
χ3544-4-400-21002-2-13-3-312-1323−2323−230003−303−300−2i2ii3i3−i3−i30000ii−i−i000000000000000
χ3644-4-400-21002-2-13-3-312-13−2323−2323000−330−33002i−2ii3i3−i3−i30000−i−iii000000000000000
χ3744-4-400-21002-2-13-3-312-13−2323−2323000−330−3300−2i2i−i3−i3i3i30000ii−i−i000000000000000
χ384-44-44-41-24i−4i1-1-2-2-222-122ii−i−i1-1i−2i−2i−i2i2i0000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000
χ394-44-44-41-24i−4i1-1-2-2-222-122ii−i−i1-1i−2i−2i−i2i2i0000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000
χ404-44-44-41-2−4i4i1-1-2-2-222-122−i−iii1-1−i2i2ii−2i−2i0000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000
χ414-44-44-41-2−4i4i1-1-2-2-222-122−i−iii1-1−i2i2ii−2i−2i0000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000
χ424-44-44-4-214i−4i-22111-1-12-1-1−2i−2i2i2i-22−2iii2i−i−i0000−i3i3−i3i300003−33−3000000000000000
χ434-44-44-4-214i−4i-22111-1-12-1-1−2i−2i2i2i-22−2iii2i−i−i0000i3−i3i3−i30000−33−33000000000000000
χ444-44-44-4-21−4i4i-22111-1-12-1-12i2i−2i−2i-222i−i−i−2iii0000−i3i3−i3i30000−33−33000000000000000
χ454-44-44-4-21−4i4i-22111-1-12-1-12i2i−2i−2i-222i−i−i−2iii0000i3−i3i3−i300003−33−3000000000000000
χ464-44-4-441-2001-1-222-22-12-23i3i−3i−3i-11−3i003i0000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ230000000
χ474-44-4-441-2001-1-222-22-12-23i3i−3i−3i-11−3i003i00000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ230000000
χ484-44-4-441-2001-1-222-22-12-2−3i−3i3i3i-113i00−3i00000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ130000000
χ494-44-4-441-2001-1-222-22-12-2−3i−3i3i3i-113i00−3i0000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ130000000
χ504-4-44004400-4-4-4000-44400000000000002-2002-2-2200000000000000000000000
χ514-4-44004400-4-4-4000-4440000000000000-2200-222-200000000000000000000000
χ524-4-4400-210022-13-33-1-21-3−2i32i32i3−2i3000−i3i30i3−i32-200-111-10000−i3i3i3−i3000000000000000
χ534-4-4400-210022-13-33-1-21-3−2i32i32i3−2i3000−i3i30i3−i3-22001-1-110000i3−i3−i3i3000000000000000
χ544-4-4400-210022-13-33-1-21-32i3−2i3−2i32i3000i3−i30−i3i32-200-111-10000i3−i3−i3i3000000000000000
χ554-4-4400-210022-13-33-1-21-32i3−2i3−2i32i3000i3−i30−i3i3-22001-1-110000−i3i3i3−i3000000000000000
χ568888-8-8-4200-4-42-2-2-22-42-20000440000000000000000000000000000000000000
χ5788-8-8002-400-224000-4-24023−2323−23000−23230−23230000000000000000000000000000000
χ5888-8-8002-400-224000-4-240−2323−232300023−23023−230000000000000000000000000000000
χ5988-8-800-42004-4-2-66624-2-60000000000000000000000000000000000000000000
χ608-88-8-88-4200-442-2-22-24-2200004-40000000000000000000000000000000000000
χ618-8-88002-400-2-2400042-40−2i32i32i3−2i30002i3−2i30−2i32i30000000000000000000000000000000
χ628-8-88002-400-2-2400042-402i3−2i3−2i32i3000−2i32i302i3−2i30000000000000000000000000000000
χ638-8-8800-420044-2-66-6-2-4260000000000000000000000000000000000000000000

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