Finite Group Databasebeta

← Group #11771238

Character table — Group #11771238

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444444444444488888888181824242424242424242424242424242424242424242424242436363672727272
order12222244334666666666612121212661212121212124444448888121212121212121224242424242424242248888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1ii−i−i
χ6111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1−i−iii
χ7111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1−i−iii
χ8111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1ii−i−i
χ91111-1-11111-11111-1-1-111-11111-1-111-1-1-1-1-1-1i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-11-11i−ii−i
χ101111-1-11111-11111-1-1-111-11111-1-111-1-1-1-1-1-1i−ii−i-11-11ii−i−iii−i−i-1-111-1-1111-11−ii−ii
χ111111-1-11111-11111-1-1-111-11111-1-111-1-1-1-1-1-1−ii−ii1-11-1−i−iii−i−iii11-1-111-1-11-11−ii−ii
χ121111-1-11111-11111-1-1-111-11111-1-111-1-1-1-1-1-1−ii−ii-11-11−i−iii−i−iii-1-111-1-1111-11i−ii−i
χ131111-1-1-1-11111111-1-1-111-1-1-1-1-1-1-1-1-1111111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-1-111-1
χ141111-1-1-1-11111111-1-1-111-1-1-1-1-1-1-1-1-1111111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i1-1-11-1-11
χ151111-1-1-1-11111111-1-1-111-1-1-1-1-1-1-1-1-1111111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii1-1-11-1-11
χ161111-1-1-1-11111111-1-1-111-1-1-1-1-1-1-1-1-1111111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-1-111-1
χ17222222222222222222222222222222222-2-2000000000000000000000000-2-2-20000
χ18222222-2-222-22222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000-2-220000
χ192222-2-22222-22222-2-2-222-22222-2-222-2-2-2-222000000000000000000000000-22-20000
χ202222-2-2-2-22222222-2-2-222-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000-2220000
χ21444444441-2411-2-21111-21-2-2-2-2-2-21111-2-20022220000-1-1-1-1-1-1-1-1000000000000000
χ22444444441-2411-2-21111-21-2-2-2-2-2-21111-2-200-2-2-2-2000011111111000000000000000
χ2344444444-214-2-211-2-2-2-21-2111111-2-2-2-211000000222200000000-1-1-1-1-1-1-1-10000000
χ2444444444-214-2-211-2-2-2-21-2111111-2-2-2-211000000-2-2-2-200000000111111110000000
χ25444444-4-41-2-411-2-21111-212222-2-2-1-1-1-1220022-2-20000-1-1-1-11111000000000000000
χ26444444-4-41-2-411-2-21111-212222-2-2-1-1-1-12200-2-22200001111-1-1-1-1000000000000000
χ27444444-4-4-21-4-2-211-2-2-2-21-2-1-1-1-1112222-1-10000002i2i−2i−2i00000000−i−i−i−iiiii0000000
χ28444444-4-4-21-4-2-211-2-2-2-21-2-1-1-1-1112222-1-1000000−2i−2i2i2i00000000iiii−i−i−i−i0000000
χ294444-4-4441-2-411-2-2-1-1-11-2-1-2-2-2-22211-1-122002i−2i2i−2i0000−i−iii−i−iii000000000000000
χ304444-4-4441-2-411-2-2-1-1-11-2-1-2-2-2-22211-1-12200−2i2i−2i2i0000ii−i−iii−i−i000000000000000
χ314444-4-444-21-4-2-211222-2121111-1-1-2-222-1-10000002-22-200000000-1-111-1-1110000000
χ324444-4-444-21-4-2-211222-2121111-1-1-2-222-1-1000000-22-220000000011-1-111-1-10000000
χ334444-4-4-4-41-2411-2-2-1-1-11-2-1222222-1-111-2-2002i−2i−2i2i0000−i−iiiii−i−i000000000000000
χ344444-4-4-4-41-2411-2-2-1-1-11-2-1222222-1-111-2-200−2i2i2i−2i0000ii−i−i−i−iii000000000000000
χ354444-4-4-4-4-214-2-211222-212-1-1-1-1-1-122-2-2110000002i−2i−2i2i00000000−i−iiiii−i−i0000000
χ364444-4-4-4-4-214-2-211222-212-1-1-1-1-1-122-2-211000000−2i2i2i−2i00000000ii−i−i−i−iii0000000
χ3744-4-400004404-44-4000-4-400000000000004i−4i0000000000000000000000000000000
χ3844-4-400004404-44-4000-4-40000000000000−4i4i0000000000000000000000000000000
χ394-44-44-400440-44-4444-4-4-4-400004-4000000000000000000000000000000000000000
χ404-44-44-400-2102-2-11-2-222-123i3i−3i−3i1-100003i−3i000000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000
χ414-44-44-400-2102-2-11-2-222-123i3i−3i−3i1-100003i−3i000000000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000
χ424-44-44-400-2102-2-11-2-222-12−3i−3i3i3i1-10000−3i3i000000000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000
χ434-44-44-400-2102-2-11-2-222-12−3i−3i3i3i1-10000−3i3i000000000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000
χ444-44-4-4400440-44-44-4-44-4-440000-44000000000000000000000000000000000000000
χ454-44-4-4400-2102-2-1122-22-1-23i3i−3i−3i-110000−3i3i000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000
χ464-44-4-4400-2102-2-1122-22-1-23i3i−3i−3i-110000−3i3i000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000
χ474-44-4-4400-2102-2-1122-22-1-2−3i−3i3i3i-1100003i−3i000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000
χ484-44-4-4400-2102-2-1122-22-1-2−3i−3i3i3i-1100003i−3i000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000
χ494-4-44004-41-20-1-1223-331-2-32-22-2001-13-3000000000000−i3i3−i3i3−i3i3−i3i3000000000000000
χ504-4-44004-41-20-1-1223-331-2-32-22-2001-13-3000000000000i3−i3i3−i3i3−i3i3−i3000000000000000
χ514-4-44004-41-20-1-122-33-31-232-22-2001-1-330000000000003−3−333−3−33000000000000000
χ524-4-44004-41-20-1-122-33-31-232-22-2001-1-33000000000000−333−3−333−3000000000000000
χ534-4-44004-4440-4-4-4-4000440-44-44004-40000000000000000000000000000000000000
χ544-4-4400-441-20-1-1223-331-2-3-22-2200-11-33000000000000−i3i3−i3i3i3−i3i3−i3000000000000000
χ554-4-4400-441-20-1-1223-331-2-3-22-2200-11-33000000000000i3−i3i3−i3−i3i3−i3i3000000000000000
χ564-4-4400-441-20-1-122-33-31-23-22-2200-113-30000000000003−3−33−333−3000000000000000
χ574-4-4400-441-20-1-122-33-31-23-22-2200-113-3000000000000−333−33−3−33000000000000000
χ584-4-4400-44440-4-4-4-40004404-44-400-440000000000000000000000000000000000000
χ5988-8-800002-402-2-446-6-6-246000000000000000000000000000000000000000000000
χ6088-8-800002-402-2-44-666-24-6000000000000000000000000000000000000000000000
χ6188-8-80000-420-442-20004-206i−6i−6i6i00000000000000000000000000000000000000000
χ6288-8-80000-420-442-20004-20−6i6i6i−6i00000000000000000000000000000000000000000
χ638-88-88-8002-40-224-422-2-24-20000-44000000000000000000000000000000000000000
χ648-88-8-88002-40-224-4-2-22-24200004-4000000000000000000000000000000000000000
χ658-8-88008-8-42044-2-2000-420-22-2200-440000000000000000000000000000000000000
χ668-8-8800-88-42044-2-2000-4202-22-2004-40000000000000000000000000000000000000

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