Finite Group Databasebeta

← Group #11770925

Character table — Group #11770925

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888121212121212121218181818181824242424242424242424242424242424242424243672727272
order12222244334666666666612121212661212121212128888888844444444441212121212121212242424242424242448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i11-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i1ii−i−i
χ6111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i1−i−iii
χ7111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii11-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii1−i−iii
χ8111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiii1ii−i−i
χ91111-1-11111-11111-1-111-1-11111-1-111-1-1-1-111-1-111-1-11111-1-1i−ii−iii−i−iii−i−i11-1-111-1-1-1i−ii−i
χ101111-1-11111-11111-1-111-1-11111-1-111-1-1-1-111-1-111-1-11111-1-1−ii−ii−i−iii−i−iii11-1-111-1-1-1−ii−ii
χ111111-1-11111-11111-1-111-1-11111-1-111-1-1-1-1-1-111-1-1111111-1-1i−ii−iii−i−iii−i−i-1-111-1-111-1−ii−ii
χ121111-1-11111-11111-1-111-1-11111-1-111-1-1-1-1-1-111-1-1111111-1-1−ii−ii−i−iii−i−iii-1-111-1-111-1i−ii−i
χ131111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii11-1-111i−i−iiii−i−i−i−iiiii−i−i−i−iii-1-111-1
χ141111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii11-1-111−iii−i−i−iiiii−i−iii−i−i−i−iii-11-1-11
χ151111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i11-1-111i−i−iiii−i−i−i−iii−i−iiiii−i−i-11-1-11
χ161111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i11-1-111−iii−i−i−iiiii−i−i−i−iiiii−i−i-1-111-1
χ1722222222222222222222222222222222200000000-2-2-2-2-2-200000000000000000000-20000
χ18222222-2-222-22222222222-2-2-2-222-2-2-2-2-2-200000000-2-2222200000000000000000000-20000
χ192222-2-22222-22222-2-222-2-22222-2-222-2-2-2-200000000-2-2-2-2220000000000000000000020000
χ202222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2-2-2222200000000-2-222-2-20000000000000000000020000
χ212-22-22-20022022-2-222-2-2-2-200002-20000002−22−22−22−2002-22-20000000000002−22−22−22−200000
χ222-22-22-20022022-2-222-2-2-2-200002-2000000−i2i2−i2i2i2−i2i2−i200-22-22000000000000−i2i2−i2i2i2−i2i2−i200000
χ232-22-22-20022022-2-222-2-2-2-200002-2000000i2−i2i2−i2−i2i2−i2i200-22-22000000000000i2−i2i2−i2−i2i2−i2i200000
χ242-22-22-20022022-2-222-2-2-2-200002-2000000−22−22−22−22002-22-2000000000000−22−22−22−2200000
χ252-22-2-220022022-2-2-2-2-2-2220000-220000002−2−222−2−22002-2-220000000000002−2−222−2−2200000
χ262-22-2-220022022-2-2-2-2-2-2220000-22000000−i2i2i2−i2i2−i2−i2i200-222-2000000000000−i2i2i2−i2i2−i2−i2i200000
χ272-22-2-220022022-2-2-2-2-2-2220000-22000000i2−i2−i2i2−i2i2i2−i200-222-2000000000000i2−i2−i2i2−i2i2i2−i200000
χ282-22-2-220022022-2-2-2-2-2-2220000-22000000−222−2−222−2002-2-22000000000000−222−2−222−200000
χ29444444441-241-21-2111-211-2-2-2-2-2-21111-2-2000000000000002222-1-1-1-1-1-1-1-10000000000000
χ30444444441-241-21-2111-211-2-2-2-2-2-21111-2-200000000000000-2-2-2-2111111110000000000000
χ3144444444-214-21-21-2-2-21-2-2111111-2-2-2-21122222222000000000000000000-1-1-1-1-1-1-1-100000
χ3244444444-214-21-21-2-2-21-2-2111111-2-2-2-211-2-2-2-2-2-2-2-20000000000000000001111111100000
χ33444444-4-41-2-41-21-2111-2112222-2-2-1-1-1-1220000000000000022-2-2-1-1-1-111110000000000000
χ34444444-4-41-2-41-21-2111-2112222-2-2-1-1-1-12200000000000000-2-2221111-1-1-1-10000000000000
χ35444444-4-4-21-4-21-21-2-2-21-2-2-1-1-1-1112222-1-12i2i2i2i−2i−2i−2i−2i000000000000000000−i−i−i−iiiii00000
χ36444444-4-4-21-4-21-21-2-2-21-2-2-1-1-1-1112222-1-1−2i−2i−2i−2i2i2i2i2i000000000000000000iiii−i−i−i−i00000
χ374444-4-4441-2-41-21-2-1-11-2-1-1-2-2-2-22211-1-122000000000000002i−2i2i−2i−i−iii−i−iii0000000000000
χ384444-4-4441-2-41-21-2-1-11-2-1-1-2-2-2-22211-1-12200000000000000−2i2i−2i2iii−i−iii−i−i0000000000000
χ394444-4-444-21-4-21-2122-21221111-1-1-2-222-1-122-2-222-2-2000000000000000000-1-111-1-11100000
χ404444-4-444-21-4-21-2122-21221111-1-1-2-222-1-1-2-222-2-22200000000000000000011-1-111-1-100000
χ414444-4-4-4-41-241-21-2-1-11-2-1-1222222-1-111-2-2000000000000002i−2i−2i2i−i−iiiii−i−i0000000000000
χ424444-4-4-4-41-241-21-2-1-11-2-1-1222222-1-111-2-200000000000000−2i2i2i−2iii−i−i−i−iii0000000000000
χ434444-4-4-4-4-214-21-2122-2122-1-1-1-1-1-122-2-2112i2i−2i−2i−2i−2i2i2i000000000000000000−i−iiiii−i−i00000
χ444444-4-4-4-4-214-21-2122-2122-1-1-1-1-1-122-2-211−2i−2i2i2i2i2i−2i−2i000000000000000000ii−i−i−i−iii00000
χ4544-4-40000440-4-4-4-4004400000000000000000000004i−4i00000000000000000000000000000
χ4644-4-40000440-4-4-4-400440000000000000000000000−4i4i00000000000000000000000000000
χ474-44-44-400-210-212-1-2-22-1223i3i−3i−3i1-100003i−3i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ1300000
χ484-44-44-400-210-212-1-2-22-1223i3i−3i−3i1-100003i−3i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ1300000
χ494-44-44-400-210-212-1-2-22-122−3i−3i3i3i1-10000−3i3i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ2300000
χ504-44-44-400-210-212-1-2-22-122−3i−3i3i3i1-10000−3i3i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ2300000
χ514-44-4-4400-210-212-1222-1-2-23i3i−3i−3i-110000−3i3i2ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ1300000
χ524-44-4-4400-210-212-1222-1-2-23i3i−3i−3i-110000−3i3i−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ1300000
χ534-44-4-4400-210-212-1222-1-2-2−3i−3i3i3i-1100003i−3i−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ2300000
χ544-44-4-4400-210-212-1222-1-2-2−3i−3i3i3i-1100003i−3i2ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ2300000
χ554-4-44004i−4i1-20-121-23-3-123-32i−2i2i−2i00i−i3i−3i00000000000000000000−i3i3−i3i33−33−30000000000000
χ564-4-44004i−4i1-20-121-23-3-123-32i−2i2i−2i00i−i3i−3i00000000000000000000i3−i3i3−i3−33−330000000000000
χ574-4-44004i−4i1-20-121-2-33-12-332i−2i2i−2i00i−i−3i3i000000000000000000003−3−33i3−i3−i3i30000000000000
χ584-4-44004i−4i1-20-121-2-33-12-332i−2i2i−2i00i−i−3i3i00000000000000000000−333−3−i3i3i3−i30000000000000
χ594-4-44004i−4i440-4-44400-4-400−4i4i−4i4i004i−4i0000000000000000000000000000000000000000000
χ604-4-4400−4i4i1-20-121-23-3-123-3−2i2i−2i2i00−ii−3i3i00000000000000000000−i3i3−i3i3−33−330000000000000
χ614-4-4400−4i4i1-20-121-23-3-123-3−2i2i−2i2i00−ii−3i3i00000000000000000000i3−i3i3−i33−33−30000000000000
χ624-4-4400−4i4i1-20-121-2-33-12-33−2i2i−2i2i00−ii3i−3i000000000000000000003−3−33−i3i3i3−i30000000000000
χ634-4-4400−4i4i1-20-121-2-33-12-33−2i2i−2i2i00−ii3i−3i00000000000000000000−333−3i3−i3−i3i30000000000000
χ644-4-4400−4i4i440-4-44400-4-4004i−4i4i−4i00−4i4i0000000000000000000000000000000000000000000
χ6588-8-800002-40-24-246-62-4-66000000000000000000000000000000000000000000000000000
χ6688-8-800002-40-24-24-662-46-6000000000000000000000000000000000000000000000000000
χ6788-8-80000-4204-24-200-42006-6-6600000000000000000000000000000000000000000000000
χ6888-8-80000-4204-24-200-4200-666-600000000000000000000000000000000000000000000000
χ698-88-88-8002-402-4-2422-24-2-20000-44000000000000000000000000000000000000000000000
χ708-88-8-88002-402-4-24-2-2-242200004-4000000000000000000000000000000000000000000000
χ718-8-88008i−8i-4204-2-42004-200−2i2i−2i2i00−4i4i0000000000000000000000000000000000000000000
χ728-8-8800−8i8i-4204-2-42004-2002i−2i2i−2i004i−4i0000000000000000000000000000000000000000000

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