Finite Group Databasebeta

← Group #10944191

Character table — Group #10944191

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222344444466666662222444444412121212121212124444666612121212121212121212121212122222444444444444246612128888
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
χ511111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-111
χ811111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111111111-1-1
χ9111111111-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-111-1-11-11-1
χ10111111111-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-111-1-1-11-11
χ11111111111-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-11-1-111-11-11
χ12111111111-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11-1-1111-11-1
χ13111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-11-1-1111-1-11
χ14111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-11-1-111-111-1
χ15111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111-111-1-1-111-1
χ16111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-11-111-1-11-1-11
χ172222222-2-222-2-2222222222-2-2-2-2222-2-2-2-2-2-22222000022-2-2-2-20000000022-2-200000000000000000000000000
χ182222222-2-222-2-22222222-2-222-2-22-2-222-2-2-2-222220000-2-222-2-200000000-2-22200000000000000000000000000
χ192222222-2-2-2-2-2-2222222222-2-222-2-2-222-2-2-2-2-2-2-2-2000022-2-22200000000-2-22200000000000000000000000000
χ202222222-2-2-2-2-2-22222222-2-22222-222-2-2-2-2-2-2-2-2-2-20000-2-222220000000022-2-200000000000000000000000000
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
χ25222222-122-2-222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-1-1-1-1111122-2-2-1-1-1-111-1-1-1-11111111100000000000000002-2-1-1110000
χ26222222-122-2-222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-1-1-1-11111-2-222-1-1-1-1111111-1-1-1-111110000000000000000-2211-1-10000
χ27222222-122-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-1-1111122-2-2111111-1-1-1-11111-1-1-1-10000000000000000-2211-1-10000
χ28222222-122-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-1-11111-2-2221111111111-1-1-1-1-1-1-1-100000000000000002-2-1-1110000
χ29222222-1-2-222-2-2-1-1-1-1-1-1-122-2-2-2-2222-2-21111-1-1-1-10000-1-11111−i3−i3i3i3−i3−i3i3i3-1-111000000000000000000−i3i3−i3i30000
χ30222222-1-2-222-2-2-1-1-1-1-1-1-122-2-2-2-2222-2-21111-1-1-1-10000-1-11111i3i3−i3−i3i3i3−i3−i3-1-111000000000000000000i3−i3i3−i30000
χ31222222-1-2-222-2-2-1-1-1-1-1-1-1-2-222-2-22-2-2221111-1-1-1-1000011-1-111−i3−i3i3i3−i3−i3i3i311-1-1000000000000000000i3−i3i3−i30000
χ32222222-1-2-222-2-2-1-1-1-1-1-1-1-2-222-2-22-2-2221111-1-1-1-1000011-1-111i3i3−i3−i3i3i3−i3−i311-1-1000000000000000000−i3i3−i3i30000
χ33222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-222111111110000-1-111-1-1−i3−i3i3i3i3i3−i3−i311-1-1000000000000000000−i3i3i3−i30000
χ34222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-222111111110000-1-111-1-1i3i3−i3−i3−i3−i3i3i311-1-1000000000000000000i3−i3−i3i30000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-222-2-211111111000011-1-1-1-1−i3−i3i3i3i3i3−i3−i3-1-111000000000000000000i3−i3−i3i30000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-222-2-211111111000011-1-1-1-1i3i3−i3−i3−i3−i3i3i3-1-111000000000000000000−i3i3i3−i30000
χ372222-2-222-2222-2-2-22-2-22200002-2-2000022-2-222-2-2000000002-2000000000000002200-2-20000-2-2220000000000
χ382222-2-222-2222-2-2-22-2-22200002-2-2000022-2-222-2-2000000002-200000000000000-2-20022000022-2-20000000000
χ392222-2-222-2-2-22-2-2-22-2-2220000-222000022-2-2-2-22200000000-22000000000000002200220000-2-2-2-20000000000
χ402222-2-222-2-2-22-2-2-22-2-2220000-222000022-2-2-2-22200000000-2200000000000000-2-200-2-2000022220000000000
χ412222-2-22-2222-22-2-22-2-2220000-22-20000-2-22222-2-200000000-220000000000002200-2-200-2-22200000000000000
χ422222-2-22-2222-22-2-22-2-2220000-22-20000-2-22222-2-200000000-22000000000000-2-200220022-2-200000000000000
χ432222-2-22-22-2-2-22-2-22-2-22200002-220000-2-222-2-222000000002-200000000000022002200-2-2-2-200000000000000
χ442222-2-22-22-2-2-22-2-22-2-22200002-220000-2-222-2-222000000002-2000000000000-2-200-2-200222200000000000000
χ452-22-22-222-200-2222-2-2-22-200000002i−2i2i−2i2-22-200000000000000000000002i−2i2i−2i2-200002i−2i2-200002i−2i0000000000
χ462-22-22-222-200-2222-2-2-22-200000002i−2i2i−2i2-22-200000000000000000000002i−2i2i−2i-220000−2i2i-220000−2i2i0000000000
χ472-22-22-222-200-2222-2-2-22-20000000−2i2i−2i2i2-22-20000000000000000000000−2i2i−2i2i2-20000−2i2i2-20000−2i2i0000000000
χ482-22-22-222-200-2222-2-2-22-20000000−2i2i−2i2i2-22-20000000000000000000000−2i2i−2i2i-2200002i−2i-2200002i−2i0000000000
χ492-22-22-22-22002-222-2-2-22-200000002i−2i−2i2i-22-2200000000000000000000002i−2i−2i2i002-22i−2i00002i−2i2-2000000000000
χ502-22-22-22-22002-222-2-2-22-200000002i−2i−2i2i-22-2200000000000000000000002i−2i−2i2i00-22−2i2i0000−2i2i-22000000000000
χ512-22-22-22-22002-222-2-2-22-20000000−2i2i2i−2i-22-220000000000000000000000−2i2i2i−2i002-2−2i2i0000−2i2i2-2000000000000
χ522-22-22-22-22002-222-2-2-22-20000000−2i2i2i−2i-22-220000000000000000000000−2i2i2i−2i00-222i−2i00002i−2i-22000000000000
χ532-22-2-2222200-2-2-2-2-2222-22-22-200000002-2-22000000002-22-20000000000000000002i−2i2i−2i00−2i2i00−2i2i0000000000
χ542-22-2-2222200-2-2-2-2-2222-22-22-200000002-2-22000000002-22-2000000000000000000−2i2i−2i2i002i−2i002i−2i0000000000
χ552-22-2-2222200-2-2-2-2-2222-2-22-2200000002-2-2200000000-22-220000000000000000002i−2i−2i2i00−2i2i002i−2i0000000000
χ562-22-2-2222200-2-2-2-2-2222-2-22-2200000002-2-2200000000-22-22000000000000000000−2i2i2i−2i002i−2i00−2i2i0000000000
χ572-22-2-222-2-20022-2-2-2222-22-2-220000000-222-2000000002-2-22000000000000002-22-20000-2200-22000000000000
χ582-22-2-222-2-20022-2-2-2222-22-2-220000000-222-2000000002-2-2200000000000000-22-2200002-2002-2000000000000
χ592-22-2-222-2-20022-2-2-2222-2-222-20000000-222-200000000-222-2000000000000002-2-220000-22002-2000000000000
χ602-22-2-222-2-20022-2-2-2222-2-222-20000000-222-200000000-222-200000000000000-222-200002-200-22000000000000
χ614444-4-4-24-4444-422-222-2-200004-4-40000-2-222-2-22200000000-2200000000000000000000000000000000000000
χ624444-4-4-24-4-4-44-422-222-2-20000-4440000-2-22222-2-2000000002-200000000000000000000000000000000000000
χ634444-4-4-2-4444-4422-222-2-20000-44-4000022-2-2-2-222000000002-200000000000000000000000000000000000000
χ644444-4-4-2-44-4-4-4422-222-2-200004-44000022-2-222-2-200000000-2200000000000000000000000000000000000000
χ6544-4-4004004i−4i0000400-4-40000000000000004i−4i002-22i−2i0000002-22-22i−2i2i−2i000000000000000000000000000000
χ6644-4-4004004i−4i0000400-4-40000000000000004i−4i00-22−2i2i000000-22-22−2i2i−2i2i000000000000000000000000000000
χ6744-4-400400−4i4i0000400-4-4000000000000000−4i4i002-2−2i2i0000002-22-2−2i2i−2i2i000000000000000000000000000000
χ6844-4-400400−4i4i0000400-4-4000000000000000−4i4i00-222i−2i000000-22-222i−2i2i−2i000000000000000000000000000000
χ6944-4-400-2004i−4i00−2i32i3-2−2i32i322000000000000000−2i2i23−232-22i−2i000000−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000
χ7044-4-400-2004i−4i00−2i32i3-2−2i32i322000000000000000−2i2i23−23-22−2i2i0000001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000
χ7144-4-400-2004i−4i002i3−2i3-22i3−2i322000000000000000−2i2i−23232-22i−2i000000−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000
χ7244-4-400-2004i−4i002i3−2i3-22i3−2i322000000000000000−2i2i−2323-22−2i2i0000001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000
χ7344-4-400-200−4i4i00−2i32i3-2−2i32i3220000000000000002i−2i−23232-2−2i2i000000−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000
χ7444-4-400-200−4i4i00−2i32i3-2−2i32i3220000000000000002i−2i−2323-222i−2i0000001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000
χ7544-4-400-200−4i4i002i3−2i3-22i3−2i3220000000000000002i−2i23−232-2−2i2i000000−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000
χ7644-4-400-200−4i4i002i3−2i3-22i3−2i3220000000000000002i−2i23−23-222i−2i0000001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000
χ774-44-44-4-24-400-44-2-2222-2200000004i−4i4i−4i-22-220000000000000000000000−2i2i−2i2i00000000000000000000000000
χ784-44-44-4-24-400-44-2-2222-220000000−4i4i−4i4i-22-2200000000000000000000002i−2i2i−2i00000000000000000000000000
χ794-44-44-4-2-44004-4-2-2222-2200000004i−4i−4i4i2-22-20000000000000000000000−2i2i2i−2i00000000000000000000000000
χ804-44-44-4-2-44004-4-2-2222-220000000−4i4i4i−4i2-22-200000000000000000000002i−2i−2i2i00000000000000000000000000
χ814-44-4-44-24400-4-4222-2-2-224-44-40000000-222-200000000-22-220000000000000000000000000000000000000000
χ824-44-4-44-24400-4-4222-2-2-22-44-440000000-222-2000000002-22-20000000000000000000000000000000000000000
χ834-44-4-44-2-4-40044222-2-2-224-4-4400000002-2-2200000000-222-20000000000000000000000000000000000000000
χ844-44-4-44-2-4-40044222-2-2-22-444-400000002-2-22000000002-2-220000000000000000000000000000000000000000
χ858-8-8800800000000-800-880000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4000000−4i34i344i3−4i34-40000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-40000004i3−4i34−4i34i34-40000000000000000000000000000000000000000000000000000000000000000000

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