Finite Group Databasebeta

← Group #10692029

Character table — Group #10692029

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
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ711111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111-1-111-1-1-11-1-1-111-1-1111-1iiii−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i1-1iiii−i−i−i−i11-1-1-1-111ii−i−iii−i−i1-111-1-1i−i1-1
χ101111-1-111-1-1-11-1-1-111-1-1111-1iiii−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i1-1iiii−i−i−i−i-1-11111-1-1−i−iii−i−iii1-111-1-1−ii-11
χ111111-1-111-1-1-11-1-1-111-1-1111-1iiii−i−i−i−i1111-1-1-1-1−i−iii−i−i−i−iiiii1-1iiii−i−i−i−i11-1-1-1-111ii−i−iii−i−i-11-1-111−ii-11
χ121111-1-111-1-1-11-1-1-111-1-1111-1iiii−i−i−i−i1111-1-1-1-1−i−iii−i−i−i−iiiii1-1iiii−i−i−i−i-1-11111-1-1−i−iii−i−iii-11-1-111i−i1-1
χ131111-1-111-1-1-11-1-1-111-1-1111-1−i−i−i−iiiii1111-1-1-1-1ii−i−iiiii−i−i−i−i1-1−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii-11-1-111i−i-11
χ141111-1-111-1-1-11-1-1-111-1-1111-1−i−i−i−iiiii1111-1-1-1-1ii−i−iiiii−i−i−i−i1-1−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i-11-1-111−ii1-1
χ151111-1-111-1-1-11-1-1-111-1-1111-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−i−i−iiiii1-1−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii1-111-1-1−ii1-1
χ161111-1-111-1-1-11-1-1-111-1-1111-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−i−i−iiiii1-1−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i1-111-1-1i−i-11
χ17222222222-2-2222222222-2-2-20000000022-2-222-2-2000000000000-2-2000000002222-2-2-2-2000000000000000000
χ18222222222-2-2222222222-2-2-20000000022-2-222-2-2000000000000-2-200000000-2-2-2-22222000000000000000000
χ192222222-2-222-2-222222222-2-222-2-222-2-2-2-222-2-222000000000000-2-222-2-222-2-200000000000000000000000000
χ202222222-2-222-2-222222222-2-2-2-222-2-222-2-222-2-222000000000000-2-2-2-222-2-22200000000000000000000000000
χ212222222-2-2-2-2-2-22222222-22200000000-2-2-2-2-2-2-2-20000000000002200000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ222222222-2-2-2-2-2-22222222-22200000000-2-2-2-2-2-2-2-2000000000000220000000000000000−2i−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
χ24222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-211111111-1-1-1-1-1-1-1-1-1-10000000000000000-2-211110000
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
χ26222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-211111111-1-111111111000000000000000022-1-1-1-10000
χ27222222-1-2-222-2-2-1-1-1-1-1-1-12-2-222-2-222-2-211-1-111-1-10000−i3−i3i3i3−i3−i3i3i311-1-111-1-111000000000000000000−i3i3−i3i30000
χ28222222-1-2-222-2-2-1-1-1-1-1-1-12-2-222-2-222-2-211-1-111-1-10000i3i3−i3−i3i3i3−i3−i311-1-111-1-111000000000000000000i3−i3i3−i30000
χ29222222-1-2-222-2-2-1-1-1-1-1-1-12-2-2-2-222-2-22211-1-111-1-10000−i3−i3i3i3−i3−i3i3i31111-1-111-1-1000000000000000000i3−i3i3−i30000
χ30222222-1-2-222-2-2-1-1-1-1-1-1-12-2-2-2-222-2-22211-1-111-1-10000i3i3−i3−i3i3i3−i3−i31111-1-111-1-1000000000000000000−i3i3−i3i30000
χ312222-2-222-2222-2-2-222-2-22-2-220000000022-2-2-2-222000000000000-220000000022-2-222-2-2000000000000000000
χ322222-2-222-2222-2-2-222-2-22-2-220000000022-2-2-2-222000000000000-2200000000-2-222-2-222000000000000000000
χ332222-2-22-2222-22-2-222-2-22-22-200000000-2-2-2-222220000000000002-200000000000000002222-2-2-2-20000000000
χ342222-2-22-2222-22-2-222-2-22-22-200000000-2-2-2-222220000000000002-20000000000000000-2-2-2-222220000000000
χ352222-2-22-22-2-2-22-2-222-2-222-222i2i−2i−2i−2i−2i2i2i-2-22222-2-2000000000000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-22-2-2-22-2-222-2-222-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-2000000000000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-12-2-2-22-211-1-111-122-22i2i2i2i−2i−2i−2i−2i-1-1-1-111112i2i−2i−2i−i−i−i−iiiii-11−i−i−i−iiiii00000000000000002-2-1-1110000
χ382222-2-2-12-2-2-22-211-1-111-122-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i-11−i−i−i−iiiii0000000000000000-2211-1-10000
χ392222-2-2-12-2-2-22-211-1-111-122-2−2i−2i−2i−2i2i2i2i2i-1-1-1-111112i2i−2i−2i−i−i−i−iiiii-11iiii−i−i−i−i0000000000000000-2211-1-10000
χ402222-2-2-12-2-2-22-211-1-111-122-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i-11iiii−i−i−i−i00000000000000002-2-1-1110000
χ412222-2-2-1-22-2-2-2211-1-111-12-222i2i−2i−2i−2i−2i2i2i11-1-1-1-111000033−3−3−3−3331-1−i−iiiii−i−i000000000000000000−i3i3i3−i30000
χ422222-2-2-1-22-2-2-2211-1-111-12-222i2i−2i−2i−2i−2i2i2i11-1-1-1-1110000−3−33333−3−31-1−i−iiiii−i−i000000000000000000i3−i3−i3i30000
χ432222-2-2-1-22-2-2-2211-1-111-12-22−2i−2i2i2i2i2i−2i−2i11-1-1-1-111000033−3−3−3−3331-1ii−i−i−i−iii000000000000000000i3−i3−i3i30000
χ442222-2-2-1-22-2-2-2211-1-111-12-22−2i−2i2i2i2i2i−2i−2i11-1-1-1-1110000−3−33333−3−31-1ii−i−i−i−iii000000000000000000−i3i3i3−i30000
χ4522-2-22-222200-2-2222-2-2-2-20002−22−22−22−22-2002-200000000000000002−22−22−22−22-22-200002−22−22−22−20000000000
χ4622-2-22-222200-2-2222-2-2-2-20002−22−22−22−22-2002-200000000000000002−22−22−22−2-22-220000−22−22−22−220000000000
χ4722-2-22-222200-2-2222-2-2-2-2000−22−22−22−222-2002-20000000000000000−22−22−22−222-22-20000−22−22−22−220000000000
χ4822-2-22-222200-2-2222-2-2-2-2000−22−22−22−222-2002-20000000000000000−22−22−22−22-22-2200002−22−22−22−20000000000
χ4922-2-22-22-2-20022222-2-2-2-20002−2−222−2−22-2200-2200000000000000002−2−222−2−2200002i−2i2i−2i−i2i2i2−i2i2−i2−i2i20000000000
χ5022-2-22-22-2-20022222-2-2-2-20002−2−222−2−22-2200-2200000000000000002−2−222−2−220000−2i2i−2i2ii2−i2−i2i2−i2i2i2−i20000000000
χ5122-2-22-22-2-20022222-2-2-2-2000−222−2−222−2-2200-220000000000000000−222−2−222−200002i−2i2i−2ii2−i2−i2i2−i2i2i2−i20000000000
χ5222-2-22-22-2-20022222-2-2-2-2000−222−2−222−2-2200-220000000000000000−222−2−222−20000−2i2i−2i2i−i2i2i2−i2i2−i2−i2i20000000000
χ5322-2-2-2222-200-22-2-22-222-2000−i2i2−i2i2i2−i2i2−i22-200-220000000000000000−i2i2−i2i2i2−i2i2−i22-2-220000−i2i2i2−i2−i2i2i2−i20000000000
χ5422-2-2-2222-200-22-2-22-222-2000−i2i2−i2i2i2−i2i2−i22-200-220000000000000000−i2i2−i2i2i2−i2i2−i2-222-20000i2−i2−i2i2i2−i2−i2i20000000000
χ5522-2-2-2222-200-22-2-22-222-2000i2−i2i2−i2−i2i2−i2i22-200-220000000000000000i2−i2i2−i2−i2i2−i2i22-2-220000i2−i2−i2i2i2−i2−i2i20000000000
χ5622-2-2-2222-200-22-2-22-222-2000i2−i2i2−i2−i2i2−i2i22-200-220000000000000000i2−i2i2−i2−i2i2−i2i2-222-20000−i2i2i2−i2−i2i2i2−i20000000000
χ5722-2-2-222-22002-2-2-22-222-2000−i2i2i2−i2i2−i2−i2i2-22002-20000000000000000−i2i2i2−i2i2−i2−i2i200002i−2i−2i2i2−22−2−22−220000000000
χ5822-2-2-222-22002-2-2-22-222-2000−i2i2i2−i2i2−i2−i2i2-22002-20000000000000000−i2i2i2−i2i2−i2−i2i20000−2i2i2i−2i−22−222−22−20000000000
χ5922-2-2-222-22002-2-2-22-222-2000i2−i2−i2i2−i2i2i2−i2-22002-20000000000000000i2−i2−i2i2−i2i2i2−i200002i−2i−2i2i−22−222−22−20000000000
χ6022-2-2-222-22002-2-2-22-222-2000i2−i2−i2i2−i2i2i2−i2-22002-20000000000000000i2−i2−i2i2−i2i2i2−i20000−2i2i2i−2i2−22−2−22−220000000000
χ61444444-244-4-444-2-2-2-2-2-2-2-4-4-400000000-2-222-2-222000000000000220000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2-4440000000022222222000000000000-2-20000000000000000000000000000000000
χ634444-4-4-24-4444-422-2-222-2-4-4400000000-2-22222-2-20000000000002-20000000000000000000000000000000000
χ644444-4-4-2-4444-4422-2-222-2-44-4000000002222-2-2-2-2000000000000-220000000000000000000000000000000000
χ6544-4-44-4-24400-4-4-2-2-2222200022−2222−2222−2222−22-2200-220000000000000000−22−22−22−2200000000000000000000000000
χ6644-4-44-4-24400-4-4-2-2-22222000−2222−2222−2222−2222-2200-2200000000000000002−22−22−22−200000000000000000000000000
χ6744-4-44-4-2-4-40044-2-2-2222200022−22−222222−22−22222-2002-20000000000000000−222−2−222−200000000000000000000000000
χ6844-4-44-4-2-4-40044-2-2-22222000−222222−22−222222−222-2002-200000000000000002−2−222−2−2200000000000000000000000000
χ6944-4-4-44-24-400-4422-22-2-22000−2i22i2−2i22i22i2−2i22i2−2i2-22002-20000000000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ7044-4-4-44-24-400-4422-22-2-220002i2−2i22i2−2i2−2i22i2−2i22i2-22002-20000000000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ7144-4-4-44-2-44004-422-22-2-22000−2i22i22i2−2i22i2−2i2−2i22i22-200-220000000000000000i2−i2−i2i2−i2i2i2−i200000000000000000000000000
χ7244-4-4-44-2-44004-422-22-2-220002i2−2i2−2i22i2−2i22i22i2−2i22-200-220000000000000000−i2i2i2−i2i2−i2−i2i200000000000000000000000000
χ734-44-4004004-40000-4400-4000000000000000004-42-22-22-22-22-22-2000000000000000000000000000000000000
χ744-44-4004004-40000-4400-4000000000000000004-4-22-22-22-22-22-22000000000000000000000000000000000000
χ754-44-400400-440000-4400-400000000000000000-442i−2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ764-44-400400-440000-4400-400000000000000000-44−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ774-44-400-2004-400−2i32i32-2−2i32i320000000000000−2i32i300-222-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000000000000
χ784-44-400-2004-400−2i32i32-2−2i32i320000000000000−2i32i300-22-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000000000000
χ794-44-400-2004-4002i3−2i32-22i3−2i3200000000000002i3−2i300-222-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000000000000
χ804-44-400-2004-4002i3−2i32-22i3−2i3200000000000002i3−2i300-22-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000000000000
χ814-44-400-200-4400−2i32i32-2−2i32i3200000000000002i3−2i3002-22i−2i−2i2i2ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ22000000000000000000000000000000000000
χ824-44-400-200-4400−2i32i32-2−2i32i3200000000000002i3−2i3002-2−2i2i2i−2i−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ22000000000000000000000000000000000000
χ834-44-400-200-44002i3−2i32-22i3−2i320000000000000−2i32i3002-22i−2i−2i2i2ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ14000000000000000000000000000000000000
χ844-44-400-200-44002i3−2i32-22i3−2i320000000000000−2i32i3002-2−2i2i2i−2i−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ14000000000000000000000000000000000000
χ858-8-8800800000000-8-80080000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4000000−4i34i3444i3−4i3-40000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-40000004i3−4i344−4i34i3-40000000000000000000000000000000000000000000000000000000000000000000

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