Finite Group Databasebeta

← Group #10696848

Character table — Group #10696848

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222222222444444444888888888888888816161616161616161616161624242424484848484848
order122222344666666644444121212128888121212122424242424242424444412121212121212128888248888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-1-1-111
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1
χ81111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111
χ92222222222222222-2-22-2-222220000-2-2-2-200000000200-222-2-200000000000000
χ102222222222222222-2-22-2-222220000-2-2-2-200000000-2002-2-22200000000000000
χ112222222-2-2222222222-2-2-2-2-2-2-2000022-2-200000000000000000000000000002i−2i
χ122222222-2-2222222222-2-2-2-2-2-2-2000022-2-20000000000000000000000000000−2i2i
χ132222222-2-22222222-2-2-222-2-2-2-20000-2-2220000000000000000000022-2-2000000
χ142222222-2-22222222-2-2-222-2-2-2-20000-2-22200000000000000000000-2-222000000
χ15222222-122-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ16222222-122-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ17222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-2-1-1-1-1111111112-2-22-1-1-1-111110000000000
χ18222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-2-1-1-1-111111111-222-21111-1-1-1-10000000000
χ19222222-122-1-1-1-1-1-1-1-2-22-2-2-1-1-1-100001111−i3−i3−i3−i3i3i3i3i3200-2-1-111−i3−i3i3i30000000000
χ20222222-122-1-1-1-1-1-1-1-2-22-2-2-1-1-1-100001111−i3−i3−i3−i3i3i3i3i3-200211-1-1i3i3−i3−i30000000000
χ21222222-122-1-1-1-1-1-1-1-2-22-2-2-1-1-1-100001111i3i3i3i3−i3−i3−i3−i3200-2-1-111i3i3−i3−i30000000000
χ22222222-122-1-1-1-1-1-1-1-2-22-2-2-1-1-1-100001111i3i3i3i3−i3−i3−i3−i3-200211-1-1−i3−i3i3i30000000000
χ232222-2-2222-2-2-2-22222-2-22-222-2-200002-22-20000000000000000000000002-20000
χ242222-2-2222-2-2-2-22222-2-22-222-2-200002-22-2000000000000000000000000-220000
χ252222-2-2222-2-2-2-2222-22-2-2222-2-20000-22-22000000000000000000000000002-200
χ262222-2-2222-2-2-2-2222-22-2-2222-2-20000-22-2200000000000000000000000000-2200
χ272222-2-22-2-2-2-2-2-22222-22-22-2-22222-2-22-2-2222-2-222-2-20000000000000000000000
χ282222-2-22-2-2-2-2-2-22222-22-22-2-222-2-2222-2-22-2-222-2-2220000000000000000000000
χ292222-2-22-2-2-2-2-2-2222-2222-2-2-2220000-222-20000000002-2000002-22-20000000000
χ302222-2-22-2-2-2-2-2-2222-2222-2-2-2220000-222-2000000000-2200000-22-220000000000
χ312222-2-2-1-2-21111-1-1-12-22-2211-1-122-2-2-111-1-1-111-1-1110000−i3i3−i3i3−i3i3i3−i30000000000
χ322222-2-2-1-2-21111-1-1-12-22-2211-1-122-2-2-111-1-1-111-1-1110000i3−i3i3−i3i3−i3−i3i30000000000
χ332222-2-2-1-2-21111-1-1-12-22-2211-1-1-2-222-111-111-1-111-1-10000−i3i3−i3i3i3−i3−i3i30000000000
χ342222-2-2-1-2-21111-1-1-12-22-2211-1-1-2-222-111-111-1-111-1-10000i3−i3i3−i3−i3i3i3−i30000000000
χ352222-2-2-1-2-21111-1-1-1-2222-211-1-100001-1-11−i3−i3i3i3i3i3−i3−i302-20−i3i3i3−i3-11-110000000000
χ362222-2-2-1-2-21111-1-1-1-2222-211-1-100001-1-11−i3−i3i3i3i3i3−i3−i30-220i3−i3−i3i31-11-10000000000
χ372222-2-2-1-2-21111-1-1-1-2222-211-1-100001-1-11i3i3−i3−i3−i3−i3i3i302-20i3−i3−i3i3-11-110000000000
χ382222-2-2-1-2-21111-1-1-1-2222-211-1-100001-1-11i3i3−i3−i3−i3−i3i3i30-220−i3i3i3−i31-11-10000000000
χ39444444-2-4-4-2-2-2-2-2-2-244-4-4-422220000-2-222000000000000000000000000000000
χ40444444-2-4-4-2-2-2-2-2-2-2-4-4-4442222000022-2-2000000000000000000000000000000
χ414444-4-4-2442222-2-2-24-4-44-4-2-2220000-22-22000000000000000000000000000000
χ424444-4-4-2442222-2-2-2-44-4-44-2-22200002-22-2000000000000000000000000000000
χ434-44-40044-40000-4-44000004-4002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ444-44-40044-40000-4-44000004-400−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ454-44-4004-440000-4-4400000-44002i−2i−2i2i00002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ464-44-4004-440000-4-4400000-4400−2i2i2i−2i0000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ474-44-400-24-4−2i3−2i32i32i322-200000-22−2i32i32i−2i2i−2i00002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ220000000000000000000000
χ484-44-400-24-4−2i3−2i32i32i322-200000-22−2i32i3−2i2i−2i2i0000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ220000000000000000000000
χ494-44-400-24-42i32i3−2i3−2i322-200000-222i3−2i32i−2i2i−2i00002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ140000000000000000000000
χ504-44-400-24-42i32i3−2i3−2i322-200000-222i3−2i3−2i2i−2i2i0000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ140000000000000000000000
χ514-44-400-2-44−2i3−2i32i32i322-2000002-22i3−2i32i−2i−2i2i00002ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ140000000000000000000000
χ524-44-400-2-44−2i3−2i32i32i322-2000002-22i3−2i3−2i2i2i−2i0000−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ140000000000000000000000
χ534-44-400-2-442i32i3−2i3−2i322-2000002-2−2i32i32i−2i−2i2i00002ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ220000000000000000000000
χ544-44-400-2-442i32i3−2i3−2i322-2000002-2−2i32i3−2i2i2i−2i0000−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ220000000000000000000000
χ554-4-444-44004-44-44-4-4000000000000000000000000000000000000000−2i22i2000000
χ564-4-444-44004-44-44-4-40000000000000000000000000000000000000002i2−2i2000000
χ574-4-44-44400-44-444-4-40000000000000000000000000000000000000−2i22i200000000
χ584-4-44-44400-44-444-4-400000000000000000000000000000000000002i2−2i200000000
χ5988-8-8008000000-88-800000000000000000000000000000000000000000000000
χ6088-8-800-400−4i34i34i3−4i34-4400000000000000000000000000000000000000000000000
χ6188-8-800-4004i3−4i3−4i34i34-4400000000000000000000000000000000000000000000000
χ628-8-888-8-400-44-44-44400000000000000000000000000000000000000000000000
χ638-8-88-88-4004-44-4-44400000000000000000000000000000000000000000000000

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