Finite Group Databasebeta

← Group #10692052

Character table — Group #10692052

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order122222344444466612121212444661212121212122444444466121212121212121212121212121212128824242424888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ91111-1-111-1-1-11-1111-1-1-1-111-1-1-11111-1-11-1-11ii−i−i111-111-1-1-1-1iiii−i−i−i−ii−iii−i−ii−ii−iii−i−i1-11-1
χ101111-1-111-1-1-11-1111-1-1-1-111-1-1-11111-1-11-1-11ii−i−i111-111-1-1-1-1iiii−i−i−i−ii−iii−i−i−ii−ii−i−iii-11-11
χ111111-1-111-1-1-11-1111-1-1-1-111-1-1-11111-1-11-1-11−i−iii111-111-1-1-1-1−i−i−i−iiiii−ii−i−iiii−ii−iii−i−i-11-11
χ121111-1-111-1-1-11-1111-1-1-1-111-1-1-11111-1-11-1-11−i−iii111-111-1-1-1-1−i−i−i−iiiii−ii−i−iii−ii−ii−i−iii1-11-1
χ131111-1-111-1-1-11-1111-1-1-1-111-1-1-11111-1-1-111-1ii−i−i-1-11-1-1-11111iiii−i−i−i−i−ii−i−iiii−ii−i−i−iii-111-1
χ141111-1-111-1-1-11-1111-1-1-1-111-1-1-11111-1-1-111-1ii−i−i-1-11-1-1-11111iiii−i−i−i−i−ii−i−iii−ii−iiii−i−i1-1-11
χ151111-1-111-1-1-11-1111-1-1-1-111-1-1-11111-1-1-111-1−i−iii-1-11-1-1-11111−i−i−i−iiiiii−iii−i−ii−ii−i−i−iii1-1-11
χ161111-1-111-1-1-11-1111-1-1-1-111-1-1-11111-1-1-111-1−i−iii-1-11-1-1-11111−i−i−i−iiiiii−iii−i−i−ii−iiii−i−i-111-1
χ172222222222-22-22222222-2-2-22222-2-2-2-222-2-2000022-2-2-2-222-2-200000000000000000000000000
χ182222222222-22-22222222-2-2-22222-2-2-2-2-2-2220000-2-2-2-222-2-22200000000000000000000000000
χ192222222-2-2-22-22222-2-2-2-22-2-222-2-2-2-22200000000002-20000000000000000000000002-22-20000
χ202222222-2-2-22-22222-2-2-2-22-2-222-2-2-2-22200000000002-2000000000000000000000000-22-220000
χ212222222-2-2-2-2-2-2222-2-2-2-2-22222-2-222-2-20000000000-22000000000000000000002i−2i−2i2i00000000
χ222222222-2-2-2-2-2-2222-2-2-2-2-22222-2-222-2-20000000000-2200000000000000000000−2i2i2i−2i00000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ25222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2222211-1-1111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ26222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211-1-11111111111111122-1-1-1-1000000000000
χ27222222-1222-22-2-1-1-1-1-1-1-1-2-2-2-1-1-1-1111122-2-20000-1-11111-1-111−i3−i3i3i3−i3−i3i3i300−i3i3−i3i3000000000000
χ28222222-1222-22-2-1-1-1-1-1-1-1-2-2-2-1-1-1-1111122-2-20000-1-11111-1-111i3i3−i3−i3i3i3−i3−i300i3−i3i3−i3000000000000
χ29222222-1222-22-2-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-2-22200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300i3−i3i3−i3000000000000
χ30222222-1222-22-2-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-2-22200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300−i3i3−i3i3000000000000
χ312222-2-222-2-2222222-2-2-2-2-2-22-2-222-2-2222-22-2000022-22-2-2-2-22200000000000000000000000000
χ322222-2-222-2-2222222-2-2-2-2-2-22-2-222-2-222-22-220000-2-2-222222-2-200000000000000000000000000
χ332222-2-22-2222-222222222-22-2-2-2-2-222220000000000-2-20000000000000000000022-2-200000000
χ342222-2-22-2222-222222222-22-2-2-2-2-222220000000000-2-200000000000000000000-2-22200000000
χ352222-2-22-222-2-2-222222222-22-2-2-2-2-2-2-2-20000000000220000000000000000000000002i−2i−2i2i0000
χ362222-2-22-222-2-2-222222222-22-2-2-2-2-2-2-2-2000000000022000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-12-2-2222-1-1-11111-2-2211-1-111-1-12-22-20000-1-11-11111-1-133−3−3−3−333003−3−33000000000000
χ382222-2-2-12-2-2222-1-1-11111-2-2211-1-111-1-12-22-20000-1-11-11111-1-1−3−33333−3−300−333−3000000000000
χ392222-2-2-12-2-2222-1-1-11111-2-2211-1-111-1-1-22-220000111-1-1-1-1-11133−3−3−3−33300−333−3000000000000
χ402222-2-2-12-2-2222-1-1-11111-2-2211-1-111-1-1-22-220000111-1-1-1-1-111−3−33333−3−3003−3−33000000000000
χ412222-2-2-12-2-2-22-2-1-1-1111122-211-1-1-1-1112-2-222i2i−2i−2i-1-1-11-1-11111−i−i−i−iiiii2i−2i−i−iii000000000000
χ422222-2-2-12-2-2-22-2-1-1-1111122-211-1-1-1-1112-2-22−2i−2i2i2i-1-1-11-1-11111iiii−i−i−i−i−2i2iii−i−i000000000000
χ432222-2-2-12-2-2-22-2-1-1-1111122-211-1-1-1-111-222-22i2i−2i−2i11-1111-1-1-1-1−i−i−i−iiiii−2i2iii−i−i000000000000
χ442222-2-2-12-2-2-22-2-1-1-1111122-211-1-1-1-111-222-2−2i−2i2i2i11-1111-1-1-1-1iiii−i−i−i−i2i−2i−i−iii000000000000
χ45444444-2-4-4-44-44-2-2-222224-4-4-2-22222-2-20000000000-2200000000000000000000000000000000
χ46444444-2-4-4-4-4-4-4-2-2-22222-444-2-222-2-22200000000002-200000000000000000000000000000000
χ474444-4-4-2-4444-44-2-2-2-2-2-2-2-44-42222-2-2-2-200000000002200000000000000000000000000000000
χ484444-4-4-2-444-4-4-4-2-2-2-2-2-2-24-44222222220000000000-2-200000000000000000000000000000000
χ4944-4-400400040-44-4-400000000000004-400002-22-200000000002-22-22-22-2000000000000000000
χ5044-4-400400040-44-4-400000000000004-40000-22-220000000000-22-22-22-22000000000000000000
χ5144-4-4004000-4044-4-40000000000000-4400002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ5244-4-4004000-4044-4-40000000000000-440000−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ5344-4-400-200040-4-22223−2323−23000000023−23-2200002-22-20000000000−1+31−3−1−31+3−1−31+3−1+31−3000000000000000000
χ5444-4-400-200040-4-22223−2323−23000000023−23-220000-22-2200000000001−3−1+31+3−1−31+3−1−31−3−1+3000000000000000000
χ5544-4-400-200040-4-222−2323−23230000000−2323-2200002-22-20000000000−1−31+3−1+31−3−1+31−3−1−31+3000000000000000000
χ5644-4-400-200040-4-222−2323−23230000000−2323-220000-22-2200000000001+3−1−31−3−1+31−3−1+31+3−1−3000000000000000000
χ5744-4-400-2000-404-22223−2323−230000000−23232-200002i−2i−2i2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000
χ5844-4-400-2000-404-22223−2323−230000000−23232-20000−2i2i2i−2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000
χ5944-4-400-2000-404-222−2323−2323000000023−232-200002i−2i−2i2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000
χ6044-4-400-2000-404-222−2323−2323000000023−232-20000−2i2i2i−2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000
χ614-44-44-444-440-40-44-4-4-4440004-44-4000000000000000000000000000000000000000000000000
χ624-44-44-44-44-4040-44-444-4-40004-4-44000000000000000000000000000000000000000000000000
χ634-44-44-4-24-440-402-2222-2-2000-22-22000000000000000023−230023−2300000000000000000000000000
χ644-44-44-4-24-440-402-2222-2-2000-22-220000000000000000−232300−232300000000000000000000000000
χ654-44-44-4-2-44-40402-22-2-222000-222-2000000000000−2i32i30000−2i32i30000000000000000000000000000
χ664-44-44-4-2-44-40402-22-2-222000-222-20000000000002i3−2i300002i3−2i30000000000000000000000000000
χ674-44-4-44444-40-40-44-444-4-4000-444-4000000000000000000000000000000000000000000000000
χ684-44-4-444-4-44040-44-4-4-444000-44-44000000000000000000000000000000000000000000000000
χ694-44-4-44-244-40-402-22-2-2220002-2-22000000000000000023−2300−232300000000000000000000000000
χ704-44-4-44-244-40-402-22-2-2220002-2-220000000000000000−23230023−2300000000000000000000000000
χ714-44-4-44-2-4-440402-2222-2-20002-22-2000000000000−2i32i300002i3−2i30000000000000000000000000000
χ724-44-4-44-2-4-440402-2222-2-20002-22-20000000000002i3−2i30000−2i32i30000000000000000000000000000
χ738-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000
χ758-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.