Finite Group Databasebeta

← Group #10692528

Character table — Group #10692528

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order1222223444444666666622444444444121212121212121244446612121212121212121212121212121212888888888888888844121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-11-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-111-1-11-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ711111111111111111111-1-111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111-1-111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111-1-1-1-1-1-111111111111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1i−ii−i
χ101111111-1-1-1-1-1-111111111111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−ii−ii
χ111111111-1-1-1-1-1-111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-111−ii−ii
χ121111111-1-1-1-1-1-111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-111i−ii−i
χ131111111-1-1-1-1-1-11111111-1-11111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii-11-1-111i−i−ii
χ141111111-1-1-1-1-1-11111111-1-11111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−iii−i
χ151111111-1-1-1-1-1-11111111-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1−iii−i
χ161111111-1-1-1-1-1-11111111-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1i−i−ii
χ1722222222222-2-2222222222-2-222-2-2-2-2-22222-2-2-2-200002200000000-2-222-2-2-2-200000000000000000000000000
χ1822222222222-2-22222222-2-2-2-2-2-2-222222222-2-2-2-20000-2-200000000-2-2-2-2222200000000000000000000000000
χ192222222-2-2-2-222222222222-2-2-2-22-2-222-2-2-2-2222200002200000000-2-2-2-2-2-22200000000000000000000000000
χ202222222-2-2-2-2222222222-2-2-2-222222-2-2-2-2-2-222220000-2-200000000-2-22222-2-200000000000000000000000000
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
χ22222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-1-2-222-2-22-2-2-2-2-1-1-1-1-1-1-1-1222211-1-1-1-1-1-1-1-1-1-11111110000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-1-2-222-2-22-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-21111111111-1-1111111000000000000000022-1-1-1-10000
χ25222222-12222-2-2-1-1-1-1-1-1-122-2-222-2-2-2-2-2-1-1-1-111110000-1-1−i3−i3i3i3−i3−i3i3i311-1-11111000000000000000000−i3i3−i3i30000
χ26222222-12222-2-2-1-1-1-1-1-1-122-2-222-2-2-2-2-2-1-1-1-111110000-1-1i3i3−i3−i3i3i3−i3−i311-1-11111000000000000000000i3−i3i3−i30000
χ27222222-12222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-1-11111000011−i3−i3i3i3−i3−i3i3i31111-1-1-1-1000000000000000000i3−i3i3−i30000
χ28222222-12222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-1-11111000011i3i3−i3−i3i3i3−i3−i31111-1-1-1-1000000000000000000−i3i3−i3i30000
χ29222222-1-2-2-2-222-1-1-1-1-1-1-122-2-2-2-22-2-2221111-1-1-1-10000-1-1−i3−i3i3i3i3i3−i3−i3111111-1-1000000000000000000−i3i3i3−i30000
χ30222222-1-2-2-2-222-1-1-1-1-1-1-122-2-2-2-22-2-2221111-1-1-1-10000-1-1i3i3−i3−i3−i3−i3i3i3111111-1-1000000000000000000i3−i3−i3i30000
χ31222222-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222222-2-21111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i311-1-1-1-111000000000000000000i3−i3−i3i30000
χ32222222-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222222-2-21111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i311-1-1-1-111000000000000000000−i3i3i3−i30000
χ33222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-222-2-21111111122-2-2-1-1-1-1-1-11111-1-111-1-11100000000000000002-2-1-1110000
χ34222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-222-2-211111111-2-222-1-11111-1-1-1-1-1-111-1-1110000000000000000-2211-1-10000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2221111111122-2-211-1-1-1-11111-1-1-1-111-1-10000000000000000-2211-1-10000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-22211111111-2-222111111-1-1-1-1-1-1-1-111-1-100000000000000002-2-1-1110000
χ372222-2-2222-2-222-2-2-2-2222002-200-2000022-2-222-2-2000000000000002-20000000000000022-2-222-2-20000000000
χ382222-2-2222-2-222-2-2-2-2222002-200-2000022-2-222-2-2000000000000002-200000000000000-2-222-2-2220000000000
χ392222-2-2222-2-2-2-2-2-2-2-222200-22002000022-2-2-2-22200000000000000-220000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ402222-2-2222-2-2-2-2-2-2-2-222200-22002000022-2-2-2-22200000000000000-22000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ412222-2-22-2-22222-2-2-2-222200-2200-20000-2-22222-2-200000000000000-2200000022-2-2-2-222000000000000000000
χ422222-2-22-2-22222-2-2-2-222200-2200-20000-2-22222-2-200000000000000-22000000-2-22222-2-2000000000000000000
χ432222-2-22-2-222-2-2-2-2-2-2222002-20020000-2-222-2-222000000000000002-2000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ442222-2-22-2-222-2-2-2-2-2-2222002-20020000-2-222-2-222000000000000002-200000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ452-22-22-222i−2i2i−2i0022-2-2-22-200000002i−2i2-22i−2i2i−2i00000000000000000000002i−2i2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ462-22-22-222i−2i2i−2i0022-2-2-22-200000002i−2i2-22i−2i2i−2i00000000000000000000002i−2i2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ472-22-22-222i−2i2i−2i0022-2-2-22-20000000−2i2i-222i−2i2i−2i0000000000000000000000−2i2i-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ482-22-22-222i−2i2i−2i0022-2-2-22-20000000−2i2i-222i−2i2i−2i0000000000000000000000−2i2i-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ492-22-22-22−2i2i−2i2i0022-2-2-22-200000002i−2i-22−2i2i−2i2i00000000000000000000002i−2i-221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ502-22-22-22−2i2i−2i2i0022-2-2-22-200000002i−2i-22−2i2i−2i2i00000000000000000000002i−2i-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ512-22-22-22−2i2i−2i2i0022-2-2-22-20000000−2i2i2-2−2i2i−2i2i0000000000000000000000−2i2i2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ522-22-22-22−2i2i−2i2i0022-2-2-22-20000000−2i2i2-2−2i2i−2i2i0000000000000000000000−2i2i2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ532-22-2-2222i−2i−2i2i00-2-222-22-22-2002i−2i000002i−2i−2i2i000000002-200000000002i−2i00001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ542-22-2-2222i−2i−2i2i00-2-222-22-22-2002i−2i000002i−2i−2i2i000000002-200000000002i−2i0000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ552-22-2-2222i−2i−2i2i00-2-222-22-2-2200−2i2i000002i−2i−2i2i00000000-220000000000−2i2i00001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ562-22-2-2222i−2i−2i2i00-2-222-22-2-2200−2i2i000002i−2i−2i2i00000000-220000000000−2i2i0000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ572-22-2-222−2i2i2i−2i00-2-222-22-22-200−2i2i00000−2i2i2i−2i000000002-20000000000−2i2i00001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ582-22-2-222−2i2i2i−2i00-2-222-22-22-200−2i2i00000−2i2i2i−2i000000002-20000000000−2i2i0000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ592-22-2-222−2i2i2i−2i00-2-222-22-2-22002i−2i00000−2i2i2i−2i00000000-2200000000002i−2i00001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ602-22-2-222−2i2i2i−2i00-2-222-22-2-22002i−2i00000−2i2i2i−2i00000000-2200000000002i−2i0000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ614444-4-4-244-4-4442222-2-2-2004-400-40000-2-222-2-22200000000000000-2200000000000000000000000000000000
χ624444-4-4-244-4-4-4-42222-2-2-200-440040000-2-22222-2-2000000000000002-200000000000000000000000000000000
χ634444-4-4-2-4-444442222-2-2-200-4400-4000022-2-2-2-222000000000000002-200000000000000000000000000000000
χ644444-4-4-2-4-444-4-42222-2-2-2004-4004000022-2-222-2-200000000000000-2200000000000000000000000000000000
χ654-44-44-4-24i−4i4i−4i00-2-2222-2200000004i−4i4-4−2i2i−2i2i0000000000000000000000−2i2i-2200000000000000000000000000
χ664-44-44-4-24i−4i4i−4i00-2-2222-220000000−4i4i-44−2i2i−2i2i00000000000000000000002i−2i2-200000000000000000000000000
χ674-44-44-4-2−4i4i−4i4i00-2-2222-2200000004i−4i-442i−2i2i−2i0000000000000000000000−2i2i2-200000000000000000000000000
χ684-44-44-4-2−4i4i−4i4i00-2-2222-220000000−4i4i4-42i−2i2i−2i00000000000000000000002i−2i-2200000000000000000000000000
χ694-44-4-44-24i−4i−4i4i0022-2-22-224-4004i−4i00000−2i2i2i−2i00000000-220000000000−2i2i000000000000000000000000000000
χ704-44-4-44-24i−4i−4i4i0022-2-22-22-4400−4i4i00000−2i2i2i−2i000000002-200000000002i−2i000000000000000000000000000000
χ714-44-4-44-2−4i4i4i−4i0022-2-22-224-400−4i4i000002i−2i−2i2i00000000-2200000000002i−2i000000000000000000000000000000
χ724-44-4-44-2−4i4i4i−4i0022-2-22-22-44004i−4i000002i−2i−2i2i000000002-20000000000−2i2i000000000000000000000000000000
χ734-4-4400400004i−4i0000-4-440000000000000004i−4i002-22i−2i002-22-22i−2i2i−2i0000000000000000000000000000000000
χ744-4-4400400004i−4i0000-4-440000000000000004i−4i00-22−2i2i00-22-22−2i2i−2i2i0000000000000000000000000000000000
χ754-4-440040000−4i4i0000-4-44000000000000000−4i4i002-2−2i2i002-22-2−2i2i−2i2i0000000000000000000000000000000000
χ764-4-440040000−4i4i0000-4-44000000000000000−4i4i00-222i−2i00-22-222i−2i2i−2i0000000000000000000000000000000000
χ774-4-4400-200004i−4i−2i32i3−2i32i322-2000000000000000−2i2i23−232-22i−2i00−1−i31+i3−1+i31−i32ζ7−2ζ72ζ11−2ζ110000000000000000000000000000000000
χ784-4-4400-200004i−4i−2i32i3−2i32i322-2000000000000000−2i2i23−23-22−2i2i001+i3−1−i31−i3−1+i3−2ζ72ζ7−2ζ112ζ110000000000000000000000000000000000
χ794-4-4400-200004i−4i2i3−2i32i3−2i322-2000000000000000−2i2i−23232-22i−2i00−1+i31−i3−1−i31+i32ζ11−2ζ112ζ7−2ζ70000000000000000000000000000000000
χ804-4-4400-200004i−4i2i3−2i32i3−2i322-2000000000000000−2i2i−2323-22−2i2i001−i3−1+i31+i3−1−i3−2ζ112ζ11−2ζ72ζ70000000000000000000000000000000000
χ814-4-4400-20000−4i4i−2i32i3−2i32i322-20000000000000002i−2i−23232-2−2i2i00−1−i31+i3−1+i31−i3−2ζ72ζ7−2ζ112ζ110000000000000000000000000000000000
χ824-4-4400-20000−4i4i−2i32i3−2i32i322-20000000000000002i−2i−2323-222i−2i001+i3−1−i31−i3−1+i32ζ7−2ζ72ζ11−2ζ110000000000000000000000000000000000
χ834-4-4400-20000−4i4i2i3−2i32i3−2i322-20000000000000002i−2i23−232-2−2i2i00−1+i31−i3−1−i31+i3−2ζ112ζ11−2ζ72ζ70000000000000000000000000000000000
χ844-4-4400-20000−4i4i2i3−2i32i3−2i322-20000000000000002i−2i23−23-222i−2i001−i3−1+i31+i3−1−i32ζ11−2ζ112ζ7−2ζ70000000000000000000000000000000000
χ8588-8-800800000000008-8-80000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-4000000−4i34i34i3−4i3-4440000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-40000004i3−4i3−4i34i3-4440000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.