Finite Group Databasebeta

← Group #10829888

Character table — Group #10829888

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222224444444444888888888888888888888888121212121616161616161616242424242424242424244848
order1222223444466644446612121212222444446612121212121212121212121212124444668824242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111-111-111-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-111-1-11-1-11-1-111
χ5111111111111111111111111-1-11111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1
χ6111111111111111111111111-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1
χ911111111111111-1-1-1-1111111111-11-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111-111-1-11-1-1-1111-1-1-11-1
χ1011111111111111-1-1-1-1111111111-11-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1111-1-1-1111-11
χ1111111111111111-1-1-1-111111111-11-11-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-11-1-111-11-1-1-1111-1-1-11
χ1211111111111111-1-1-1-111111111-11-11-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11-1-1111-1111-1-1-1111-1
χ1311111111111111-1-1-1-1111111-1-11-11-11111-1-111-1-1-1-1-1-111111111-1-1-11-1-1111-1-1-11-1-1-111-11
χ1411111111111111-1-1-1-1111111-1-11-11-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-111-1111-1111-1-11-1
χ1511111111111111-1-1-1-1111111-1-1-11-1111-1-111-1-1-1-1-1-11111111111-1-11-111-1-1-11-1-1-1-1-11111-1
χ1611111111111111-1-1-1-1111111-1-1-11-1111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11-111-1-11-111111-1-1-1-11
χ172222222-2-2-2-222222-2-222-2-2-2-20000000000000022-2-200000022-2-200000000002-200000000
χ182222222-2-2-2-222222-2-222-2-2-2-20000000000000022-2-2000000-2-2220000000000-2200000000
χ192222222-2-2-2-2222-2-22222-2-2-2-200000000000000-2-22200000022-2-20000000000-2200000000
χ202222222-2-2-2-2222-2-22222-2-2-2-200000000000000-2-222000000-2-22200000000002-200000000
χ21222222-12222-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-122-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-122-2-2-2-222111111-1-1-1-111-1-1-1-10000-1-1-2-21111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-11111000011-2-21111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111-1-1-1-111111100001122-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1222-22-2-2-2-1-111-1-111111111110000-1-12-2-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-122-22-22-2-211-1-1111111-1-111110000-1-1-2211-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22-22-222-1-111-1-1111111-1-1-1-1000011-2211-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2-22-222211-1-1111111-1-1-1-1-1-10000112-2-1-111000000000000
χ292222-2-222-22-22220000-2-22-22-200020-2000022000000-2-200002-22-2000000000200000-20000
χ302222-2-222-22-22220000-2-22-22-200020-2000022000000-2-20000-22-22000000000-20000020000
χ312222-2-222-22-22220000-2-22-22-2000-2020000-2-20000002200002-22-2000000000-20000020000
χ322222-2-222-22-22220000-2-22-22-2000-2020000-2-2000000220000-22-22000000000200000-20000
χ332222-2-22-22-222220000-2-2-22-220020-20002200-2-200000000002-2-22000000002000-20000000
χ342222-2-22-22-222220000-2-2-22-220020-20002200-2-20000000000-222-200000000-200020000000
χ352222-2-22-22-222220000-2-2-22-2200-202000-2-2002200000000002-2-2200000000-200020000000
χ362222-2-22-22-222220000-2-2-22-2200-202000-2-200220000000000-222-2000000002000-20000000
χ372-22-2-2222-2-22-22-22i−2i2i−2i2-22-2-222-200002i−2i0000002i−2i2i−2i002i2i−2i−2i00002-2000000000000000000
χ382-22-2-2222-2-22-22-22i−2i2i−2i2-22-2-22-220000−2i2i0000002i−2i2i−2i00−2i−2i2i2i0000-22000000000000000000
χ392-22-2-2222-2-22-22-2−2i2i−2i2i2-22-2-222-20000−2i2i000000−2i2i−2i2i00−2i−2i2i2i00002-2000000000000000000
χ402-22-2-2222-2-22-22-2−2i2i−2i2i2-22-2-22-2200002i−2i000000−2i2i−2i2i002i2i−2i−2i0000-22000000000000000000
χ412-22-2-222-222-2-22-22i−2i−2i2i2-2-222-2000000000000002i−2i−2i2i000000000000000000000002i−2i02-200
χ422-22-2-222-222-2-22-22i−2i−2i2i2-2-222-2000000000000002i−2i−2i2i00000000000000000000000−2i2i0-2200
χ432-22-2-222-222-2-22-2−2i2i2i−2i2-2-222-200000000000000−2i2i2i−2i000000000000000000000002i−2i0-2200
χ442-22-2-222-222-2-22-2−2i2i2i−2i2-2-222-200000000000000−2i2i2i−2i00000000000000000000000−2i2i02-200
χ452-22-2-22-12-2-221-112i−2i2i−2i-11-111-12-200002i−2i−i3i33−3−i3i3−ii−ii3−3−i−iii0000-1100−i3i33−3000000000000
χ462-22-2-22-12-2-221-112i−2i2i−2i-11-111-12-200002i−2ii3−i3−33i3−i3−ii−ii−33−i−iii0000-1100i3−i3−33000000000000
χ472-22-2-22-12-2-221-112i−2i2i−2i-11-111-1-220000−2i2i−i3i33−3−i3i3−ii−ii3−3ii−i−i00001-100i3−i3−33000000000000
χ482-22-2-22-12-2-221-112i−2i2i−2i-11-111-1-220000−2i2ii3−i3−33i3−i3−ii−ii−33ii−i−i00001-100−i3i33−3000000000000
χ492-22-2-22-12-2-221-11−2i2i−2i2i-11-111-12-20000−2i2i−i3i3−33−i3i3i−ii−i−33ii−i−i0000-1100−i3i3−33000000000000
χ502-22-2-22-12-2-221-11−2i2i−2i2i-11-111-12-20000−2i2ii3−i33−3i3−i3i−ii−i3−3ii−i−i0000-1100i3−i33−3000000000000
χ512-22-2-22-12-2-221-11−2i2i−2i2i-11-111-1-2200002i−2i−i3i3−33−i3i3i−ii−i−33−i−iii00001-100i3−i33−3000000000000
χ522-22-2-22-12-2-221-11−2i2i−2i2i-11-111-1-2200002i−2ii3−i33−3i3−i3i−ii−i3−3−i−iii00001-100−i3i3−33000000000000
χ53444444-2-4-4-4-4-2-2-244-4-4-2-2222200000000000000-2-222000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-444-2-222220000000000000022-2-2000000000000000000000000000000
χ554444-4-4-24-44-4-2-2-2000022-22-2200040-40000-2-2000000220000000000000000000000000000
χ564444-4-4-24-44-4-2-2-2000022-22-22000-404000022000000-2-20000000000000000000000000000
χ574444-4-4-2-44-44-2-2-20000222-22-20040-4000-2-200220000000000000000000000000000000000
χ584444-4-4-2-44-44-2-2-20000222-22-200-4040002200-2-20000000000000000000000000000000000
χ594-44-44-4444-4-4-44-40000-4444-4-4000000000000000000000000000000000000000000000000
χ604-44-44-44-4-444-44-40000-44-4-444000000000000000000000000000000000000000000000000
χ614-44-44-4-244-4-42-2200002-2-2-222000000000023−23000000−23230000000000000000000000000000
χ624-44-44-4-244-4-42-2200002-2-2-2220000000000−232300000023−230000000000000000000000000000
χ634-44-44-4-2-4-4442-2200002-222-2-200000000−2i32i3002i3−2i30000000000000000000000000000000000
χ644-44-44-4-2-4-4442-2200002-222-2-2000000002i3−2i300−2i32i30000000000000000000000000000000000
χ654-44-4-44-2-444-42-224i−4i−4i4i-222-2-2200000000000000−2i2i2i−2i000000000000000000000000000000
χ664-44-4-44-2-444-42-22−4i4i4i−4i-222-2-22000000000000002i−2i−2i2i000000000000000000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-44400000000000000000000000000000023−2323−23000000000000000000000000
χ6988-8-800-40000-444000000000000000000000000000000−2323−2323000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-4000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ728-8-8800-4000044-40000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000

Here i is the imaginary unit (i² = −1).