Finite Group Databasebeta

← Group #10713972

Character table — Group #10713972

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222222222222222224444444444444448888888888888888888888888888888888884848484848484848
order122223444468812122424242466688812121224242424242424668812121616161616161616242424244848484848484848484848484848484822444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-111
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ922222222222-2-222-2-2-2-2222-2-2-2222-2-2-2-2-2-22222-2-22200000000-2-2-2-2000000000000000000000000
χ1022222222222-2-222-2-2-2-2222-2-2-2222-2-2-2-2-2-2-2-2-2-222-2-2000000002222000000000000000000000000
χ1122222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-122-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1222222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-122-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000
χ1322222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-211-2-2112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000
χ1422222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-211-2-211-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000
χ1522222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-111111122-1-1-2-2-1-10000000011113333−3−3−3−33333−3−3−3−300000000
χ1622222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-111111122-1-1-2-2-1-1000000001111−3−3−3−33333−3−3−3−3333300000000
χ1722222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-1111111-2-211221100000000-1-1-1-13333−3−3−3−3−3−3−3−3333300000000
χ1822222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-1111111-2-211221100000000-1-1-1-1−3−3−3−333333333−3−3−3−300000000
χ19222-2-2222-2-2200-2-200002-2-200022-200000000002i−2i00−i2−i2i2i222−2−22i2i−2i−2i−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000
χ20222-2-2222-2-2200-2-200002-2-200022-200000000002i−2i00i2i2−i2−i2−2−2222i2i−2i−2ii2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000
χ21222-2-2222-2-2200-2-200002-2-200022-20000000000−2i2i00−i2−i2i2i2−2−222−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000
χ22222-2-2222-2-2200-2-200002-2-200022-20000000000−2i2i00i2i2−i2−i222−2−2−2i−2i2i2ii2i2−i2−i2i2i2−i2−i222−2−222−2−200000000
χ23222-2-22-2-2222222222222-2-22-2-2-2-2222-2-2-2-20000000000000000000000000000000000000000002-2
χ24222-2-22-2-2222222222222-2-22-2-2-2-2222-2-2-2-2000000000000000000000000000000000000000000-22
χ25222-2-22-2-2222-2-222-2-2-2-22-2-2-222-2-22-2-22222000000000000000000000000000000000000020-20000
χ26222-2-22-2-2222-2-222-2-2-2-22-2-2-222-2-22-2-222220000000000000000000000000000000000000-2020000
χ27222-2-2-122-2-2-1001133−3−3-111000-1-113−33−33−300−i3i32i−2i−i3i3−i2−i2i2i222−2−2−i−iiiζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000
χ28222-2-2-122-2-2-1001133−3−3-111000-1-113−33−33−300−i3i32i−2i−i3i3i2i2−i2−i2−2−222−i−iii−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000
χ29222-2-2-122-2-2-1001133−3−3-111000-1-113−33−33−300i3−i3−2i2ii3−i3−i2−i2i2i2−2−222ii−i−iζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000
χ30222-2-2-122-2-2-1001133−3−3-111000-1-113−33−33−300i3−i3−2i2ii3−i3i2i2−i2−i222−2−2ii−i−i−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000
χ31222-2-2-122-2-2-10011−3−333-111000-1-11−33−33−3300−i3i3−2i2i−i3i3−i2−i2i2i2−2−222ii−i−iζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000
χ32222-2-2-122-2-2-10011−3−333-111000-1-11−33−33−3300−i3i3−2i2i−i3i3i2i2−i2−i222−2−2ii−i−i−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000
χ33222-2-2-122-2-2-10011−3−333-111000-1-11−33−33−3300i3−i32i−2ii3−i3−i2−i2i2i222−2−2−i−iiiζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000
χ34222-2-2-122-2-2-10011−3−333-111000-1-11−33−33−3300i3−i32i−2ii3−i3i2i2−i2−i2−2−222−i−iii−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000
χ3522-22-222-22-2222222222-22-2-2-222-2-2-2-2-2-2220000000000002-22-20000000000002-22-22-22-200000000
χ3622-22-222-22-2222222222-22-2-2-222-2-2-2-2-2-222000000000000-22-22000000000000-22-22-22-2200000000
χ3722-22-222-22-22-2-222-2-2-2-2-22-222-22-2-22222-2-2000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ3822-22-222-22-22-2-222-2-2-2-2-22-222-22-2-22222-2-200000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ3922-22-2-12-22-2-122-1-1-1-1-1-11-11-2-22-1111111-1-100−i3i300i3−i300002-22-2−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3-11-11-11-1100000000
χ4022-22-2-12-22-2-122-1-1-1-1-1-11-11-2-22-1111111-1-100−i3i300i3−i30000-22-22−i3i3−i3i3i3−i3i3−i3−i3i3−i3i31-11-11-11-100000000
χ4122-22-2-12-22-2-122-1-1-1-1-1-11-11-2-22-1111111-1-100i3−i300−i3i300002-22-2i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3-11-11-11-1100000000
χ4222-22-2-12-22-2-122-1-1-1-1-1-11-11-2-22-1111111-1-100i3−i300−i3i30000-22-22i3−i3i3−i3−i3i3−i3i3i3−i3i3−i31-11-11-11-100000000
χ4322-22-2-12-22-2-1-2-2-1-111111-1122-2-111-1-1-1-11100−i3i300i3−i32i−2i2i−2i0000i3−i3i3−i3−ii−ii−ii−ii3−33−3−33−3300000000
χ4422-22-2-12-22-2-1-2-2-1-111111-1122-2-111-1-1-1-11100−i3i300i3−i3−2i2i−2i2i0000i3−i3i3−i3i−ii−ii−ii−i−33−333−33−300000000
χ4522-22-2-12-22-2-1-2-2-1-111111-1122-2-111-1-1-1-11100i3−i300−i3i32i−2i2i−2i0000−i3i3−i3i3−ii−ii−ii−ii−33−333−33−300000000
χ4622-22-2-12-22-2-1-2-2-1-111111-1122-2-111-1-1-1-11100i3−i300−i3i3−2i2i−2i2i0000−i3i3−i3i3i−ii−ii−ii−i3−33−3−33−3300000000
χ4722-2-2222-2-22200-2-20000-2-220002-220000002-22200-2-22−2−22−222−200002−2−222−2−22−222−2−222−200000000
χ4822-2-2222-2-22200-2-20000-2-220002-220000002-22200-2-2−222−22−2−220000−222−2−222−22−2−222−2−2200000000
χ4922-2-2222-2-22200-2-20000-2-220002-22000000-22-2-200222−2−222−2−2200002−2−222−2−222−2−222−2−2200000000
χ5022-2-2222-2-22200-2-20000-2-220002-22000000-22-2-20022−222−2−222−20000−222−2−222−2−222−2−222−200000000
χ5122-2-222-222-2222222222-2-22-22-2-22-2-2-222-2-200000000000000000000000000000000000000002-200
χ5222-2-222-222-2222222222-2-22-22-2-22-2-2-222-2-20000000000000000000000000000000000000000-2200
χ5322-2-222-222-22-2-222-2-2-2-2-2-222-22-22-222-2-22200000000000000000000000000000000000020-200000
χ5422-2-222-222-22-2-222-2-2-2-2-2-222-22-22-222-2-222000000000000000000000000000000000000-20200000
χ5522-2-22-12-2-22-1001133−3−311-1000-11-1−33−333−32-2-1-100112−2−22−222−23−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ5622-2-22-12-2-22-1001133−3−311-1000-11-1−33−333−32-2-1-10011−222−22−2−223−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ5722-2-22-12-2-22-1001133−3−311-1000-11-1−33−333−3-221100-1-12−2−222−2−22−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ5822-2-22-12-2-22-1001133−3−311-1000-11-1−33−333−3-221100-1-1−222−2−222−2−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ5922-2-22-12-2-22-10011−3−33311-1000-11-13−33−3−332-2-1-100112−2−22−222−2−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ6022-2-22-12-2-22-10011−3−33311-1000-11-13−33−3−332-2-1-10011−222−22−2−22−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ6122-2-22-12-2-22-10011−3−33311-1000-11-13−33−3−33-221100-1-12−2−222−2−223−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ6222-2-22-12-2-22-10011−3−33311-1000-11-13−33−3−33-221100-1-1−222−2−222−23−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ63444444-4-4-4-4400-4-40000444000-4-4-400000000000000000000000000000000000000000000000000
χ6444444-2-4-4-4-4-200222323−23−23-2-2-200022223−23−2323−232300000000000000000000000000000000000000000000
χ6544444-2-4-4-4-4-20022−23−232323-2-2-2000222−232323−2323−2300000000000000000000000000000000000000000000
χ66444-4-4-2-4-444-244-2-2-2-2-2-2-2224-4-422-2-2-2222200000000000000000000000000000000000000000000
χ67444-4-4-2-4-444-2-4-4-2-22222-222-44422-222-2-2-2-200000000000000000000000000000000000000000000
χ6844-44-44-44-44400-4-40000-44-4000-44400000000000000000000000000000000000000000000000000
χ6944-44-4-2-44-44-200222323−23−232-220002-2-2−232323−23−232300000000000000000000000000000000000000000000
χ7044-44-4-2-44-44-20022−23−2323232-220002-2-223−23−232323−2300000000000000000000000000000000000000000000
χ7144-4-44-2-444-4-244-2-2-2-2-2-222-2-44-42-2222-2-22200000000000000000000000000000000000000000000
χ7244-4-44-2-444-4-2-4-4-2-2222222-24-442-22-2-222-2-200000000000000000000000000000000000000000000
χ738-800080000-8−4i24i200−4i24i2−4i24i200000000000000000000000000000000000000000000000000000000000
χ748-800080000-84i2−4i2004i2−4i24i2−4i200000000000000000000000000000000000000000000000000000000000
χ758-8000-400004−4i24i243−434ζ5+4ζ7−4ζ5−4ζ74ζ13+4ζ23−4ζ13−4ζ2300000000000000000000000000000000000000000000000000000000000
χ768-8000-400004−4i24i2−43434ζ13+4ζ23−4ζ13−4ζ234ζ5+4ζ7−4ζ5−4ζ700000000000000000000000000000000000000000000000000000000000
χ778-8000-4000044i2−4i243−43−4ζ5−4ζ74ζ5+4ζ7−4ζ13−4ζ234ζ13+4ζ2300000000000000000000000000000000000000000000000000000000000
χ788-8000-4000044i2−4i2−4343−4ζ13−4ζ234ζ13+4ζ23−4ζ5−4ζ74ζ5+4ζ700000000000000000000000000000000000000000000000000000000000

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