Finite Group Databasebeta

← Group #10707449

Character table — Group #10707449

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111222222222244888888888888888888888888888816161616161616164848484848484848
order122222366666664444444444441212121212121212121212121212121212124412121212121224888888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-11111-1-111-1-111-1-1
χ61111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-11111-1-1-1-111-1-111
χ71111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-1-111
χ81111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-11111-1-1
χ9222222222222222222-2-20000-2-2222222-2-2-2-20000000000-2-2000000000000
χ102222222222222222-2-2220000-2-222-2-2-2-222220000000000-2-2000000000000
χ1122222222222222-2-2000000222-2-2-200000000000022220-22-200-2-200000000
χ1222222222222222-2-2000000-2-22-2-2-2000000000000-2-2-2-2022-2002200000000
χ1322222222222222-2-200002200-22-2-20000000022220000-20-22-2-20000000000
χ1422222222222222-2-20000-2-200-22-2-200000000-2-2-2-2000020-22220000000000
χ15222222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000
χ16222222-1-1-1-1-1-1-1-1222222-2-2-2-222-1-1-1-1-1-1-1-1-1-111111111-2-2-1-1111100000000
χ17222222-1-1-1-1-1-1-1-12222-2-20000-2-2-1-1-1-1-1-11111−i3−i3i3i3−i3−i3i3i30011−i3i3−i3i300000000
χ18222222-1-1-1-1-1-1-1-12222-2-20000-2-2-1-1-1-1-1-11111i3i3−i3−i3i3i3−i3−i30011i3−i3i3−i300000000
χ19222222-1-1-1-1-1-1-1-122-2-2220000-2-2-1-11111-1-1-1-1−i3−i3i3i3i3i3−i3−i30011−i3i3i3−i300000000
χ20222222-1-1-1-1-1-1-1-122-2-2220000-2-2-1-11111-1-1-1-1i3i3−i3−i3−i3−i3i3i30011i3−i3−i3i300000000
χ21222222-1-1-1-1-1-1-1-122-2-2-2-222-2-222-1-111111111-1-1-1-111112-2-1-1-1-11100000000
χ22222222-1-1-1-1-1-1-1-122-2-2-2-2-2-22222-1-1111111111111-1-1-1-1-22-1-111-1-100000000
χ23222222-1-1-1-1-1-1-1-1-2-2000000222-211−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-1-1-10-2-11i3−i31100000000
χ24222222-1-1-1-1-1-1-1-1-2-2000000222-211i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-1-1-10-2-11−i3i31100000000
χ25222222-1-1-1-1-1-1-1-1-2-2000000-2-22-211−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3111102-11−i3i3-1-100000000
χ26222222-1-1-1-1-1-1-1-1-2-2000000-2-22-211i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3111102-11i3−i3-1-100000000
χ27222222-1-1-1-1-1-1-1-1-2-200002200-2211−i3−i3i3i3i3i3−i3−i3-1-1-1-1−i3−i3i3i3-201-111i3−i300000000
χ28222222-1-1-1-1-1-1-1-1-2-200002200-2211i3i3−i3−i3−i3−i3i3i3-1-1-1-1i3i3−i3−i3-201-111−i3i300000000
χ29222222-1-1-1-1-1-1-1-1-2-20000-2-200-2211−i3−i3i3i3i3i3−i3−i31111i3i3−i3−i3201-1-1-1−i3i300000000
χ30222222-1-1-1-1-1-1-1-1-2-20000-2-200-2211i3i3−i3−i3−i3−i3i3i31111−i3−i3i3i3201-1-1-1i3−i300000000
χ312-2-222-2222-22-2-2-2-222-2000000002-22-22-2000000000000000000000000−i2i2−i2i2
χ322-2-222-2222-22-2-2-2-222-2000000002-22-22-2000000000000000000000000i2−i2i2−i2
χ332-2-222-2222-22-2-2-2-22-22000000002-2-22-22000000000000000000000000−i2i2i2−i2
χ342-2-222-2222-22-2-2-2-22-22000000002-2-22-22000000000000000000000000i2−i2−i2i2
χ354444-4-44-4-444-4-44000000000000000000000000000000000000002-2000000
χ364444-4-44-4-444-4-4400000000000000000000000000000000000000-22000000
χ374-44-400400-4-400400002-22i−2i2i−2i000000002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000
χ384-44-400400-4-400400002-2−2i2i−2i2i000000002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000
χ394-44-400400-4-40040000-222i−2i−2i2i00000000-22-222i−2i2i−2i−2i2i−2i2i0000000000000000
χ404-44-400400-4-40040000-22−2i2i2i−2i00000000-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000
χ414-44-400-2−2i32i322−2i32i3-200002-22i−2i2i−2i00000000−1−i31+i3−1+i31−i32ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ22−2ζ220000000000000000
χ424-44-400-2−2i32i322−2i32i3-200002-2−2i2i−2i2i00000000−1−i31+i3−1+i31−i3−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ222ζ220000000000000000
χ434-44-400-2−2i32i322−2i32i3-20000-222i−2i−2i2i000000001+i3−1−i31−i3−1+i32ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ220000000000000000
χ444-44-400-2−2i32i322−2i32i3-20000-22−2i2i2i−2i000000001+i3−1−i31−i3−1+i3−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ220000000000000000
χ454-44-400-22i3−2i3222i3−2i3-200002-22i−2i2i−2i00000000−1+i31−i3−1−i31+i32ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ14−2ζ140000000000000000
χ464-44-400-22i3−2i3222i3−2i3-200002-2−2i2i−2i2i00000000−1+i31−i3−1−i31+i3−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ142ζ140000000000000000
χ474-44-400-22i3−2i3222i3−2i3-20000-222i−2i−2i2i000000001−i3−1+i31+i3−1−i32ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ140000000000000000
χ484-44-400-22i3−2i3222i3−2i3-20000-22−2i2i2i−2i000000001−i3−1+i31+i3−1−i3−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ140000000000000000
χ494-4-444-4444-44-4-4-44-40000000000-4400000000000000000000000000000000
χ504-4-444-4-2-2-22-22224-400000000002-2−2i32i32i3−2i30000000000000000000000000000
χ514-4-444-4-2-2-22-22224-400000000002-22i3−2i3−2i32i30000000000000000000000000000
χ524-4-444-4-2-2-22-2222-444-400000000-22-22-220000000000000000000000000000
χ534-4-444-4-2-2-22-2222-44-4400000000-222-22-20000000000000000000000000000
χ544-4-44-444-4-4-4444-400000000000000000000000000000000000000002-20000
χ554-4-44-444-4-4-4444-40000000000000000000000000000000000000000-220000
χ568888-8-8-444-4-444-40000000000000000000000000000000000000000000000
χ5788-8-8008008-800-80000000000000000000000000000000000000000000000
χ5888-8-800-4−4i34i3-444i3−4i340000000000000000000000000000000000000000000000
χ5988-8-800-44i3−4i3-44−4i34i340000000000000000000000000000000000000000000000
χ608-8-88-88-4444-4-4-440000000000000000000000000000000000000000000000

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