Finite Group Databasebeta

← Group #10693264

Character table — Group #10693264

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order122234444666244446612121212121212122244444412121212121212121212888866881212242424248888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-111-1-11-1-1-1-11-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111-1-111-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ6111111111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1
χ911111-1-1-1-11111-111-111-1-1-1-1-1-1111-1111-1-1-111111-1-1-1-1-1ii−i−i1-11-11-111-1-1i−iii−i−ii−ii−i
χ1011111-1-1-1-11111-111-111-1-1-1-1-1-1111-1111-1-1-111111-1-1-1-1-1−i−iii1-11-11-111-1-1−ii−i−iii−ii−ii
χ1111111-1-1-1-11111-111-111-1-1-1-1-1-1111-1-1-11-1111-1-1-1-1-11111ii−i−i1-1-111-1-1-111i−iii−i−i−ii−ii
χ1211111-1-1-1-11111-111-111-1-1-1-1-1-1111-1-1-11-1111-1-1-1-1-11111−i−iii1-1-111-1-1-111−ii−i−iiii−ii−i
χ1311111-1-1-1-11111-111-111-1-1-1-1-1-111-1111-11-1-111111-1-1-1-1-1ii−i−i-11-11-11-1-111i−i−i−iiii−i−ii
χ1411111-1-1-1-11111-111-111-1-1-1-1-1-111-1111-11-1-111111-1-1-1-1-1−i−iii-11-11-11-1-111−iiii−i−i−iii−i
χ1511111-1-1-1-11111-111-111-1-1-1-1-1-111-11-1-1-11111-1-1-1-1-11111ii−i−i-111-1-1111-1-1i−i−i−iii−iii−i
χ1611111-1-1-1-11111-111-111-1-1-1-1-1-111-11-1-1-11111-1-1-1-1-11111−i−iii-111-1-1111-1-1−iiii−i−ii−i−ii
χ17222222222222-2-22-2-2-2-222-2-222-2-20000000020000-2000022220000000000-2-200000000
χ18222222222222-2-22-2-2-2-222-2-222-2-20000000020000-20000-2-2-2-200000000002200000000
χ192222222-2-222222-2-2-2222222-2-2-2-200000000-20000-2000000000000000000002i−2i2i−2i0000
χ202222222-2-222222-2-2-2222222-2-2-2-200000000-20000-200000000000000000000−2i2i−2i2i0000
χ212222222-2-2222-2-2-222-2-222-2-2-2-2222200-2-200-200002000000002200-2-200000000000000
χ222222222-2-2222-2-2-222-2-222-2-2-2-222-2-2002200-20000200000000-2-2002200000000000000
χ2322222-2-2222222-2-2-2222-2-2-2-222-2-200000000-200002000000000000000000002-2-220000
χ2422222-2-2222222-2-2-2222-2-2-2-222-2-200000000-20000200000000000000000000-222-20000
χ2522222-2-222222-22-22-2-2-2-2-22222222-200-2200-20000-2000000002-200-2200000000000000
χ2622222-2-222222-22-22-2-2-2-2-2222222-22002-200-20000-200000000-22002-200000000000000
χ2722222-2-2-2-2222-222-22-2-2-2-222-2-2-2-20000000020000200002i2i−2i−2i0000000000−2i2i00000000
χ2822222-2-2-2-2222-222-22-2-2-2-222-2-2-2-2000000002000020000−2i−2i2i2i00000000002i−2i00000000
χ292222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-1-122-1-1-1-1-1-10000000000
χ302222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-122-2-222-2-2-11111-111110000-1-1-2-2-1-111110000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-1-1-1-1-1-1000011-2-21111110000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-11111-111110000112211-1-1-1-10000000000
χ332222-122-2-2-1-1-1-2-2-22211-1-11111-1-12200-2-2001−i3−i3i3i3-1−i3−i3i3i30000-1-10011−i3i3−i3i30000000000
χ342222-122-2-2-1-1-1-2-2-22211-1-11111-1-12200-2-2001i3i3−i3−i3-1i3i3−i3−i30000-1-10011i3−i3i3−i30000000000
χ352222-122-2-2-1-1-1-2-2-22211-1-11111-1-1-2-20022001−i3−i3i3i3-1−i3−i3i3i300001100-1-1i3−i3i3−i30000000000
χ362222-122-2-2-1-1-1-2-2-22211-1-11111-1-1-2-20022001i3i3−i3−i3-1i3i3−i3−i300001100-1-1−i3i3−i3i30000000000
χ372222-1-2-222-1-1-1-22-22-21111-1-1-1-1-1-12-200-22001−i3−i3i3i31i3i3−i3−i30000-11001-1−i3i3i3−i30000000000
χ382222-1-2-222-1-1-1-22-22-21111-1-1-1-1-1-12-200-22001i3i3−i3−i31−i3−i3i3i30000-11001-1i3−i3−i3i30000000000
χ392222-1-2-222-1-1-1-22-22-21111-1-1-1-1-1-1-22002-2001−i3−i3i3i31i3i3−i3−i300001-100-11i3−i3−i3i30000000000
χ402222-1-2-222-1-1-1-22-22-21111-1-1-1-1-1-1-22002-2001i3i3−i3−i31−i3−i3i3i300001-100-11−i3i3i3−i30000000000
χ412222-1-2-2-2-2-1-1-12-222-2-1-1111111-1-12-2222-2-2-2-1-1-1-1-1111110000-112-2-11-1-1110000000000
χ422222-1-2-2-2-2-1-1-12-222-2-1-1111111-1-12-2-2-22-222-111111-1-1-1-10000-11-22-1111-1-10000000000
χ432222-1-2-2-2-2-1-1-12-222-2-1-1111111-1-1-2222-22-2-2-1-1-1-1-11111100001-1-221-111-1-10000000000
χ442222-1-2-2-2-2-1-1-12-222-2-1-1111111-1-1-22-2-2-2222-111111-1-1-1-100001-12-21-1-1-1110000000000
χ454444-24444-2-2-2-4-44-4-422-2-222-2-22200000000-2000020000000000000000000000000000
χ464444-244-4-4-2-2-244-4-4-4-2-2-2-2-2-22222000000002000020000000000000000000000000000
χ474444-2-4-444-2-2-24-4-4-44-2-22222-2-2220000000020000-20000000000000000000000000000
χ484444-2-4-4-4-4-2-2-2-444-442222-2-2222200000000-20000-20000000000000000000000000000
χ4944-4-444-4004-4-400000004-400000000000000000000000022−2222−2200000000000000000000
χ5044-4-444-4004-4-400000004-4000000000000000000000000−2222−222200000000000000000000
χ5144-4-44-44004-4-40000000-44000000000000000000000000−2i22i22i2−2i200000000000000000000
χ5244-4-44-44004-4-40000000-440000000000000000000000002i2−2i2−2i22i200000000000000000000
χ534-44-44004i−4i-44-4000000000004i−4i00002-2002i−2i02-22-202i−2i2i−2i000000000000000000000000
χ544-44-44004i−4i-44-4000000000004i−4i0000-2200−2i2i0-22-220−2i2i−2i2i000000000000000000000000
χ554-44-4400−4i4i-44-400000000000−4i4i00002-200−2i2i02-22-20−2i2i−2i2i000000000000000000000000
χ564-44-4400−4i4i-44-400000000000−4i4i0000-22002i−2i0-22-2202i−2i2i−2i000000000000000000000000
χ574-44-4-2004i−4i2-2200000000023−23−2i2i−2i32i3002-2002i−2i0−1−i31+i3−1+i31−i302ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ584-44-4-2004i−4i2-2200000000023−23−2i2i−2i32i300-2200−2i2i01+i3−1−i31−i3−1+i30−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ594-44-4-2004i−4i2-22000000000−2323−2i2i2i3−2i3002-2002i−2i0−1+i31−i3−1−i31+i302ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ604-44-4-2004i−4i2-22000000000−2323−2i2i2i3−2i300-2200−2i2i01−i3−1+i31+i3−1−i30−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ614-44-4-200−4i4i2-2200000000023−232i−2i2i3−2i3002-200−2i2i0−1+i31−i3−1−i31+i30−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ624-44-4-200−4i4i2-2200000000023−232i−2i2i3−2i300-22002i−2i01−i3−1+i31+i3−1−i302ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ634-44-4-200−4i4i2-22000000000−23232i−2i−2i32i3002-200−2i2i0−1−i31+i3−1+i31−i30−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ644-44-4-200−4i4i2-22000000000−23232i−2i−2i32i300-22002i−2i01+i3−1−i31−i3−1+i302ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ6588-8-8-48-800-4440000000-44000000000000000000000000000000000000000000000000
χ6688-8-8-4-8800-44400000004-4000000000000000000000000000000000000000000000000
χ678-8-8880000-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-88-4000044-400000−4i34i300000000000000000000000000000000000000000000000000
χ698-8-88-4000044-4000004i3−4i300000000000000000000000000000000000000000000000000

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