Finite Group Databasebeta

← Group #10692036

Character table — Group #10692036

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222344444466666664448888888812121212121212124444121212121212121212122424242424242424224444448888888844121212128888
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
χ511111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111-1-111-1-1-11-1-1-111-1-1111-1iiii−i−i−i−i11-111-1-1-1ii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i1-111-1-1i−i1-1
χ101111-1-111-1-1-11-1-1-111-1-1111-1iiii−i−i−i−i11-111-1-1-1ii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii1-111-1-1−ii-11
χ111111-1-111-1-1-11-1-1-111-1-1111-1iiii−i−i−i−i11-111-1-1-1−i−iii1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i-11-1-111−ii-11
χ121111-1-111-1-1-11-1-1-111-1-1111-1iiii−i−i−i−i11-111-1-1-1−i−iii1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii-11-1-111i−i1-1
χ131111-1-111-1-1-11-1-1-111-1-1111-1−i−i−i−iiiii11-111-1-1-1ii−i−i1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii-11-1-111i−i-11
χ141111-1-111-1-1-11-1-1-111-1-1111-1−i−i−i−iiiii11-111-1-1-1ii−i−i1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i-11-1-111−ii1-1
χ151111-1-111-1-1-11-1-1-111-1-1111-1−i−i−i−iiiii11-111-1-1-1−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii1-111-1-1−ii1-1
χ161111-1-111-1-1-11-1-1-111-1-1111-1−i−i−i−iiiii11-111-1-1-1−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i1-111-1-1i−i-11
χ17222222222-2-2222222222-2-2-200000000-2-2-22222-20000-2-2000000000000000022-2-2-2-222000000000000000000
χ18222222222-2-2222222222-2-2-200000000-2-2-22222-20000-2-20000000000000000-2-22222-2-2000000000000000000
χ192222222-2-222-2-222222222-2-222-2-222-2-2222-2-2-2-220000-2-20000000022-2-222-2-200000000000000000000000000
χ202222222-2-222-2-222222222-2-2-2-222-2-222222-2-2-2-220000-2-200000000-2-222-2-22200000000000000000000000000
χ212222222-2-2-2-2-2-22222222-22200000000-2-2-2-2-2-2-2-20000220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ222222222-2-2-2-2-2-22222222-22200000000-2-2-2-2-2-2-2-2000022000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ23222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ24222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ25222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ26222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111111111111000000000000000022-1-1-1-10000
χ27222222-1-2-222-2-2-1-1-1-1-1-1-12-2-222-2-222-2-2-1-1-11111-1000011−i3−i3i3i3−i3−i3i3i3-1-111-1-111000000000000000000−i3i3−i3i30000
χ28222222-1-2-222-2-2-1-1-1-1-1-1-12-2-222-2-222-2-2-1-1-11111-1000011i3i3−i3−i3i3i3−i3−i3-1-111-1-111000000000000000000i3−i3i3−i30000
χ29222222-1-2-222-2-2-1-1-1-1-1-1-12-2-2-2-222-2-222-1-1-11111-1000011−i3−i3i3i3−i3−i3i3i311-1-111-1-1000000000000000000i3−i3i3−i30000
χ30222222-1-2-222-2-2-1-1-1-1-1-1-12-2-2-2-222-2-222-1-1-11111-1000011i3i3−i3−i3i3i3−i3−i311-1-111-1-1000000000000000000−i3i3−i3i30000
χ312222-2-222-2222-2-2-222-2-22-2-2200000000-2-2222-2-220000-22000000000000000022-2-222-2-2000000000000000000
χ322222-2-222-2222-2-2-222-2-22-2-2200000000-2-2222-2-220000-220000000000000000-2-222-2-222000000000000000000
χ332222-2-22-2222-22-2-222-2-22-22-200000000-2-22-2-222200002-20000000000000000000000002222-2-2-2-20000000000
χ342222-2-22-2222-22-2-222-2-22-22-200000000-2-22-2-222200002-2000000000000000000000000-2-2-2-222220000000000
χ352222-2-22-22-2-2-22-2-222-2-222-222i2i−2i−2i−2i−2i2i2i22-2-2-222-20000-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-22-2-2-22-2-222-2-222-22−2i−2i2i2i2i2i−2i−2i22-2-2-222-20000-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-12-2-2-22-211-1-111-122-22i2i2i2i−2i−2i−2i−2i-1-11-1-11112i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii00000000000000002-2-1-1110000
χ382222-2-2-12-2-2-22-211-1-111-122-22i2i2i2i−2i−2i−2i−2i-1-11-1-1111−2i−2i2i2i-11iiii−i−i−i−i−i−i−i−iiiii0000000000000000-2211-1-10000
χ392222-2-2-12-2-2-22-211-1-111-122-2−2i−2i−2i−2i2i2i2i2i-1-11-1-11112i2i−2i−2i-11−i−i−i−iiiiiiiii−i−i−i−i0000000000000000-2211-1-10000
χ402222-2-2-12-2-2-22-211-1-111-122-2−2i−2i−2i−2i2i2i2i2i-1-11-1-1111−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i00000000000000002-2-1-1110000
χ412222-2-2-1-22-2-2-2211-1-111-12-222i2i−2i−2i−2i−2i2i2i-1-1111-1-1100001-133−3−3−3−333−i−iiiii−i−i000000000000000000−i3i3i3−i30000
χ422222-2-2-1-22-2-2-2211-1-111-12-222i2i−2i−2i−2i−2i2i2i-1-1111-1-1100001-1−3−33333−3−3−i−iiiii−i−i000000000000000000i3−i3−i3i30000
χ432222-2-2-1-22-2-2-2211-1-111-12-22−2i−2i2i2i2i2i−2i−2i-1-1111-1-1100001-133−3−3−3−333ii−i−i−i−iii000000000000000000i3−i3−i3i30000
χ442222-2-2-1-22-2-2-2211-1-111-12-22−2i−2i2i2i2i2i−2i−2i-1-1111-1-1100001-1−3−33333−3−3ii−i−i−i−iii000000000000000000−i3i3i3−i30000
χ452-2-222-222-200-2222-2-2-2-22000−i2i2−i2i2−i2i2−i2i20002-22-2000000000000000−i2i2−i2i2−i2i2−i2i2002i−2i2i−2i002−22−22−22−20000000000
χ462-2-222-222-200-2222-2-2-2-22000−i2i2−i2i2−i2i2−i2i20002-22-2000000000000000−i2i2−i2i2−i2i2−i2i200−2i2i−2i2i00−22−22−22−220000000000
χ472-2-222-222-200-2222-2-2-2-22000i2−i2i2−i2i2−i2i2−i20002-22-2000000000000000i2−i2i2−i2i2−i2i2−i2002i−2i2i−2i00−22−22−22−220000000000
χ482-2-222-222-200-2222-2-2-2-22000i2−i2i2−i2i2−i2i2−i20002-22-2000000000000000i2−i2i2−i2i2−i2i2−i200−2i2i−2i2i002−22−22−22−20000000000
χ492-2-222-22-22002-222-2-2-2-22000−i2i2i2−i2−i2i2i2−i2000-22-22000000000000000−i2i2i2−i2−i2i2i2−i22-200002-2−i2i2i2−i2i2−i2−i2i20000000000
χ502-2-222-22-22002-222-2-2-2-22000−i2i2i2−i2−i2i2i2−i2000-22-22000000000000000−i2i2i2−i2−i2i2i2−i2-220000-22i2−i2−i2i2−i2i2i2−i20000000000
χ512-2-222-22-22002-222-2-2-2-22000i2−i2−i2i2i2−i2−i2i2000-22-22000000000000000i2−i2−i2i2i2−i2−i2i22-200002-2i2−i2−i2i2−i2i2i2−i20000000000
χ522-2-222-22-22002-222-2-2-2-22000i2−i2−i2i2i2−i2−i2i2000-22-22000000000000000i2−i2−i2i2i2−i2−i2i2-220000-22−i2i2i2−i2i2−i2−i2i20000000000
χ532-2-22-2222200-2-2-2-2-2-22220002−22−2−22−220002-2-220000000000000002−22−2−22−22002i−2i−2i2i00i2−i2−i2i2i2−i2−i2i20000000000
χ542-2-22-2222200-2-2-2-2-2-22220002−22−2−22−220002-2-220000000000000002−22−2−22−2200−2i2i2i−2i00−i2i2i2−i2−i2i2i2−i20000000000
χ552-2-22-2222200-2-2-2-2-2-2222000−22−222−22−20002-2-22000000000000000−22−222−22−2002i−2i−2i2i00−i2i2i2−i2−i2i2i2−i20000000000
χ562-2-22-2222200-2-2-2-2-2-2222000−22−222−22−20002-2-22000000000000000−22−222−22−200−2i2i2i−2i00i2−i2−i2i2i2−i2−i2i20000000000
χ572-2-22-222-2-20022-2-2-2-22220002−2−22−222−2000-222-20000000000000002−2−22−222−22-20000-222−22−2−22−220000000000
χ582-2-22-222-2-20022-2-2-2-22220002−2−22−222−2000-222-20000000000000002−2−22−222−2-2200002-2−22−222−22−20000000000
χ592-2-22-222-2-20022-2-2-2-2222000−222−22−2−22000-222-2000000000000000−222−22−2−222-20000-22−22−222−22−20000000000
χ602-2-22-222-2-20022-2-2-2-2222000−222−22−2−22000-222-2000000000000000−222−22−2−22-2200002-22−22−2−22−220000000000
χ61444444-244-4-444-2-2-2-2-2-2-2-4-4-400000000222-2-2-2-22000022000000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2-44400000000222222220000-2-2000000000000000000000000000000000000000000
χ634444-4-4-24-4444-422-2-222-2-4-440000000022-2-2-222-200002-2000000000000000000000000000000000000000000
χ644444-4-4-2-4444-4422-2-222-2-44-40000000022-222-2-2-20000-22000000000000000000000000000000000000000000
χ6544-4-4004004-400004-400-4000000000000040000-42-22-2002-22-22-22-20000000000000000000000000000000000
χ6644-4-4004004-400004-400-4000000000000040000-4-22-2200-22-22-22-220000000000000000000000000000000000
χ6744-4-400400-4400004-400-40000000000000-4000042i−2i−2i2i002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000
χ6844-4-400400-4400004-400-40000000000000-400004−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000
χ6944-4-400-2004-400−2i32i3-22−2i32i3200000000000−2i32i3-2000022-22-200−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000000000000000000000
χ7044-4-400-2004-400−2i32i3-22−2i32i3200000000000−2i32i3-200002-22-22001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000000000000000000000
χ7144-4-400-2004-4002i3−2i3-222i3−2i32000000000002i3−2i3-2000022-22-200−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000000000000000000000
χ7244-4-400-2004-4002i3−2i3-222i3−2i32000000000002i3−2i3-200002-22-22001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000000000000000000000
χ7344-4-400-200-4400−2i32i3-22−2i32i32000000000002i3−2i320000-22i−2i−2i2i002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ220000000000000000000000000000000000
χ7444-4-400-200-4400−2i32i3-22−2i32i32000000000002i3−2i320000-2−2i2i2i−2i00−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ220000000000000000000000000000000000
χ7544-4-400-200-44002i3−2i3-222i3−2i3200000000000−2i32i320000-22i−2i−2i2i002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ140000000000000000000000000000000000
χ7644-4-400-200-44002i3−2i3-222i3−2i3200000000000−2i32i320000-2−2i2i2i−2i00−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ140000000000000000000000000000000000
χ774-4-444-4-24-400-44-2-22222-2000−2i22i2−2i22i2−2i22i2−2i22i2000-22-22000000000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ784-4-444-4-24-400-44-2-22222-20002i2−2i22i2−2i22i2−2i22i2−2i2000-22-22000000000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ794-4-444-4-2-44004-4-2-22222-2000−2i22i22i2−2i2−2i22i22i2−2i20002-22-2000000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000
χ804-4-444-4-2-44004-4-2-22222-20002i2−2i2−2i22i22i2−2i2−2i22i20002-22-2000000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000
χ814-4-44-44-24400-4-42222-2-2-200022−2222−22−2222−2222000-222-2000000000000000−22−222−22−200000000000000000000000000
χ824-4-44-44-24400-4-42222-2-2-2000−2222−222222−2222−22000-222-20000000000000002−22−2−22−2200000000000000000000000000
χ834-4-44-44-2-4-400442222-2-2-200022−22−2222−222222−220002-2-22000000000000000−222−22−2−2200000000000000000000000000
χ844-4-44-44-2-4-400442222-2-2-2000−222222−2222−22−22220002-2-220000000000000002−2−22−222−200000000000000000000000000
χ858-88-800800000000-8800-80000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-4000000−4i34i34-44i3−4i340000000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-40000004i3−4i34-4−4i34i340000000000000000000000000000000000000000000000000000000000000000000

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