Finite Group Databasebeta

← Group #10692553

Character table — Group #10692553

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order12222234444446666666222244444441212121212121212444466661212121212121212121212121212888888888888888844121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111-1-1-1-1-1-1111111111-1-111-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1i−ii−i
χ101111111-1-1-1-1-1-1111111111-1-111-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−ii−ii
χ111111111-1-1-1-1-1-1111111111-1-111-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-111−ii−ii
χ121111111-1-1-1-1-1-1111111111-1-111-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-111i−ii−i
χ131111111-1-1-1-1-1-11111111-1-11111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11-1-111i−i−ii
χ141111111-1-1-1-1-1-11111111-1-11111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−iii−i
χ151111111-1-1-1-1-1-11111111-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1−iii−i
χ161111111-1-1-1-1-1-11111111-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1i−i−ii
χ17222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2222200002222-2-200000000-2-2-2-200000000000000000000000000
χ18222222222-2-2222222222-2-2-2-2-2-2-22222-2-2-2-222220000-2-2-2-2-2-200000000222200000000000000000000000000
χ192222222-2-222-2-2222222222-2-2-2-22-2-2222222-2-2-2-2000022-2-2-2-200000000-2-22200000000000000000000000000
χ202222222-2-222-2-22222222-2-222-2-2222-2-22222-2-2-2-20000-2-222-2-20000000022-2-200000000000000000000000000
χ21222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ22222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-1-1-1-10000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-122221111-1-1-1-1-1-1-1-1-1-111110000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111111111111000000000000000022-1-1-1-10000
χ25222222-122-2-222-1-1-1-1-1-1-12222-2-2-2-2-2-2-21111-1-1-1-10000-1-1-1-111−i3−i3i3i3−i3−i3i3i31111000000000000000000−i3i3−i3i30000
χ26222222-122-2-222-1-1-1-1-1-1-12222-2-2-2-2-2-2-21111-1-1-1-10000-1-1-1-111i3i3−i3−i3i3i3−i3−i31111000000000000000000i3−i3i3−i30000
χ27222222-122-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-222221111-1-1-1-10000111111−i3−i3i3i3−i3−i3i3i3-1-1-1-1000000000000000000i3−i3i3−i30000
χ28222222-122-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-222221111-1-1-1-10000111111i3i3−i3−i3i3i3−i3−i3-1-1-1-1000000000000000000−i3i3−i3i30000
χ29222222-1-2-222-2-2-1-1-1-1-1-1-122-2-2-2-22-2-222-1-1-1-111110000-1-11111−i3−i3i3i3i3i3−i3−i311-1-1000000000000000000−i3i3i3−i30000
χ30222222-1-2-222-2-2-1-1-1-1-1-1-122-2-2-2-22-2-222-1-1-1-111110000-1-11111i3i3−i3−i3−i3−i3i3i311-1-1000000000000000000i3−i3−i3i30000
χ31222222-1-2-222-2-2-1-1-1-1-1-1-1-2-222-2-2222-2-2-1-1-1-11111000011-1-111−i3−i3i3i3i3i3−i3−i3-1-111000000000000000000i3−i3−i3i30000
χ32222222-1-2-222-2-2-1-1-1-1-1-1-1-2-222-2-2222-2-2-1-1-1-11111000011-1-111i3i3−i3−i3−i3−i3i3i3-1-111000000000000000000−i3i3i3−i30000
χ33222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-222-2-21111111122-2-2-1-111-1-1-1-1-1-11111-1-11100000000000000002-2-1-1110000
χ34222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-222-2-211111111-2-222-1-111-1-11111-1-1-1-1-1-1110000000000000000-2211-1-10000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2221111111122-2-211-1-1-1-1-1-1-1-1111111-1-10000000000000000-2211-1-10000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-22211111111-2-22211-1-1-1-11111-1-1-1-111-1-100000000000000002-2-1-1110000
χ372222-2-222-2222-2-2-22-2-22200002-2-2000022-2-222-2-2000000002-20000000000000000000022-2-222-2-20000000000
χ382222-2-222-2222-2-2-22-2-22200002-2-2000022-2-222-2-2000000002-200000000000000000000-2-222-2-2220000000000
χ392222-2-222-2-2-22-2-2-22-2-2220000-2220000-2-22222-2-200000000-220000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ402222-2-222-2-2-22-2-2-22-2-2220000-2220000-2-22222-2-200000000-22000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ412222-2-22-2222-22-2-22-2-2220000-22-2000022-2-2-2-22200000000-2200000000000022-2-2-2-222000000000000000000
χ422222-2-22-2222-22-2-22-2-2220000-22-2000022-2-2-2-22200000000-22000000000000-2-22222-2-2000000000000000000
χ432222-2-22-22-2-2-22-2-22-2-22200002-220000-2-222-2-222000000002-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ442222-2-22-22-2-2-22-2-22-2-22200002-220000-2-222-2-222000000002-200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ452-2-222-222-200-2222-2-2-2-2200000002i−2i2i−2i00002-22-20000000000000000002i−2i2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000
χ462-2-222-222-200-2222-2-2-2-2200000002i−2i2i−2i00002-22-20000000000000000002i−2i2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000
χ472-2-222-222-200-2222-2-2-2-220000000−2i2i−2i2i00002-22-2000000000000000000−2i2i−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000
χ482-2-222-222-200-2222-2-2-2-220000000−2i2i−2i2i00002-22-2000000000000000000−2i2i−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000
χ492-2-222-22-22002-222-2-2-2-2200000002i−2i−2i2i0000-22-220000000000000000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000
χ502-2-222-22-22002-222-2-2-2-2200000002i−2i−2i2i0000-22-220000000000000000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000
χ512-2-222-22-22002-222-2-2-2-220000000−2i2i2i−2i0000-22-22000000000000000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000
χ522-2-222-22-22002-222-2-2-2-220000000−2i2i2i−2i0000-22-22000000000000000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000
χ532-2-22-2222200-2-2-2-2-222-222-22-2000000000002-2-2200002-22-200000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000
χ542-2-22-2222200-2-2-2-2-222-222-22-2000000000002-2-2200002-22-200000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000
χ552-2-22-2222200-2-2-2-2-222-22-22-22000000000002-2-220000-22-2200000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000
χ562-2-22-2222200-2-2-2-2-222-22-22-22000000000002-2-220000-22-2200000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000
χ572-2-22-222-2-20022-2-2-222-222-2-2200000000000-222-200002-2-22000000000000002−2−22−222−22−2−22−222−20000000000
χ582-2-22-222-2-20022-2-2-222-222-2-2200000000000-222-200002-2-2200000000000000−222−22−2−22−222−22−2−220000000000
χ592-2-22-222-2-20022-2-2-222-22-222-200000000000-222-20000-222-2000000000000002−2−22−222−2−222−22−2−220000000000
χ602-2-22-222-2-20022-2-2-222-22-222-200000000000-222-20000-222-200000000000000−222−22−2−222−2−22−222−20000000000
χ614444-4-4-24-4444-422-222-2-200004-4-40000-2-222-2-22200000000-2200000000000000000000000000000000000000
χ624444-4-4-24-4-4-44-422-222-2-20000-444000022-2-2-2-222000000002-200000000000000000000000000000000000000
χ634444-4-4-2-4444-4422-222-2-20000-44-40000-2-22222-2-2000000002-200000000000000000000000000000000000000
χ644444-4-4-2-44-4-4-4422-222-2-200004-44000022-2-222-2-200000000-2200000000000000000000000000000000000000
χ654-44-4004004-40000-4004-4000000000004-40000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ664-44-4004004-40000-4004-4000000000004-4000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ674-44-400400-440000-4004-400000000000-440000002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ684-44-400400-440000-4004-400000000000-44000000−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ694-44-400-2004-400−2i32i32−2i32i3-2200000000000-22−2i32i300002i−2i2i−2i0000002ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ14−2ζ14000000000000000000000000000000
χ704-44-400-2004-400−2i32i32−2i32i3-2200000000000-22−2i32i30000−2i2i−2i2i000000−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14000000000000000000000000000000
χ714-44-400-2004-4002i3−2i322i3−2i3-2200000000000-222i3−2i300002i−2i2i−2i0000002ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ22−2ζ22000000000000000000000000000000
χ724-44-400-2004-4002i3−2i322i3−2i3-2200000000000-222i3−2i30000−2i2i−2i2i000000−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22000000000000000000000000000000
χ734-44-400-200-4400−2i32i32−2i32i3-22000000000002-22i3−2i300002i−2i−2i2i0000002ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ14000000000000000000000000000000
χ744-44-400-200-4400−2i32i32−2i32i3-22000000000002-22i3−2i30000−2i2i2i−2i000000−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ14000000000000000000000000000000
χ754-44-400-200-44002i3−2i322i3−2i3-22000000000002-2−2i32i300002i−2i−2i2i0000002ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ22000000000000000000000000000000
χ764-44-400-200-44002i3−2i322i3−2i3-22000000000002-2−2i32i30000−2i2i2i−2i000000−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ22000000000000000000000000000000
χ774-4-444-4-24-400-44-2-22222-200000004i−4i4i−4i0000-22-22000000000000000000−2i2i−2i2i00000000000000000000000000
χ784-4-444-4-24-400-44-2-22222-20000000−4i4i−4i4i0000-22-220000000000000000002i−2i2i−2i00000000000000000000000000
χ794-4-444-4-2-44004-4-2-22222-200000004i−4i−4i4i00002-22-2000000000000000000−2i2i2i−2i00000000000000000000000000
χ804-4-444-4-2-44004-4-2-22222-20000000−4i4i4i−4i00002-22-20000000000000000002i−2i−2i2i00000000000000000000000000
χ814-4-44-44-24400-4-4222-2-22-24-44-400000000000-222-20000-22-220000000000000000000000000000000000000000
χ824-4-44-44-24400-4-4222-2-22-2-44-4400000000000-222-200002-22-20000000000000000000000000000000000000000
χ834-4-44-44-2-4-40044222-2-22-24-4-44000000000002-2-220000-222-20000000000000000000000000000000000000000
χ844-4-44-44-2-4-40044222-2-22-2-444-4000000000002-2-2200002-2-220000000000000000000000000000000000000000
χ8588-8-800800000000800-8-80000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-4000000−4i34i3-44i3−4i3440000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-40000004i3−4i3-4−4i34i3440000000000000000000000000000000000000000000000000000000000000000000

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