Finite Group Databasebeta

← Group #10694589

Character table — Group #10694589

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order12222234444444466644668888888812121212121212128888888812122424242424242424444444448888448812121212242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ91111-1-11-1-1-1-111-1-111111-1-1iiii−i−i−i−i-1-111-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-11-1i−i11-1-1ii−i−i1-1i−i
χ101111-1-11-1-1-1-111-1-111111-1-1iiii−i−i−i−i-1-111-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1-11−ii-1-111−i−iii-11−ii
χ111111-1-11-1-1-1-111-1-111111-1-1iiii−i−i−i−i-1-111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-1111-1i−i11-1-1ii−i−i-11−ii
χ121111-1-11-1-1-1-111-1-111111-1-1iiii−i−i−i−i-1-111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-111-11−ii-1-111−i−iii1-1i−i
χ131111-1-11-1-1-1-111-1-111111-1-1−i−i−i−iiiii-1-111-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-11-1−ii11-1-1−i−iii1-1−ii
χ141111-1-11-1-1-1-111-1-111111-1-1−i−i−i−iiiii-1-111-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1-11i−i-1-111ii−i−i-11i−i
χ151111-1-11-1-1-1-111-1-111111-1-1−i−i−i−iiiii-1-111-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1−ii11-1-1−i−iii-11i−i
χ161111-1-11-1-1-1-111-1-111111-1-1−i−i−i−iiiii-1-111-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-111-11i−i-1-111ii−i−i1-1−ii
χ17222222222-2-2-2-2-2-2222-22222i2i−2i−2i2i2i−2i−2i22-2-2-2-2-2-2000000002-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ18222222222-2-2-2-2-2-2222-2222−2i−2i2i2i−2i−2i2i2i22-2-2-2-2-2-2000000002-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ192222222-2-22222-2-2222-2-22200000000-2-22222-2-222222222-2-20000000000000000-2-2-2-20000000000000000
χ202222222-2-22222-2-2222-2-22200000000-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000
χ212222222-2-2-2-2-2-2222222-22200000000-2-2-2-2-2-22200000000-220000000022-2-222-2-200000000000000000000
χ222222222-2-2-2-2-2-2222222-22200000000-2-2-2-2-2-22200000000-2200000000-2-222-2-22200000000000000000000
χ23222222-122222222-1-1-122-1-122222222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ24222222-122222222-1-1-122-1-122222222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ25222222-122222222-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-1-11111111100000000000022-2-2-1-1-1-111110000
χ26222222-122222222-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-1-111111111000000000000-2-2221111-1-1-1-10000
χ27222222-122-2-2-2-2-2-2-1-1-1-22-1-12i2i−2i−2i2i2i−2i−2i-1-111111100000000-11−i−iii−i−iii0000000000000000−i3i3−i3i33−33−30000
χ28222222-122-2-2-2-2-2-2-1-1-1-22-1-12i2i−2i−2i2i2i−2i−2i-1-111111100000000-11−i−iii−i−iii0000000000000000i3−i3i3−i3−33−330000
χ29222222-122-2-2-2-2-2-2-1-1-1-22-1-1−2i−2i2i2i−2i−2i2i2i-1-111111100000000-11ii−i−iii−i−i0000000000000000−i3i3−i3i3−33−330000
χ30222222-122-2-2-2-2-2-2-1-1-1-22-1-1−2i−2i2i2i−2i−2i2i2i-1-111111100000000-11ii−i−iii−i−i0000000000000000i3−i3i3−i33−33−30000
χ312222-2-222222-2-2-2-22222-2-2-20000000022-2-222-2-200000000-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ322222-2-222222-2-2-2-22222-2-2-20000000022-2-222-2-200000000-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ332222-2-2222-2-22222222-2-2-2-2000000002222-2-2222222-2-2-2-2-2-20000000000000000-2-2220000000000000000
χ342222-2-2222-2-22222222-2-2-2-2000000002222-2-222-2-2-2-22222-2-2000000000000000022-2-20000000000000000
χ352222-2-22-2-222-2-222222-22-2-222-2-2-2-222-2-2-2-22222000000002-222-2-2-2-2220000000000000000000000000000
χ362222-2-22-2-222-2-222222-22-2-2-2-22222-2-2-2-2-2-22222000000002-2-2-22222-2-20000000000000000000000000000
χ372222-2-2-1-2-222-2-222-1-1-1-221122-2-2-2-2221111-1-1-1-100000000-11-1-11111-1-10000000000000000−i3i3i3−i3−i3i3i3−i30000
χ382222-2-2-1-2-222-2-222-1-1-1-221122-2-2-2-2221111-1-1-1-100000000-11-1-11111-1-10000000000000000i3−i3−i3i3i3−i3−i3i30000
χ392222-2-2-1-2-222-2-222-1-1-1-2211-2-22222-2-21111-1-1-1-100000000-1111-1-1-1-1110000000000000000−i3i3i3−i3i3−i3−i3i30000
χ402222-2-2-1-2-222-2-222-1-1-1-2211-2-22222-2-21111-1-1-1-100000000-1111-1-1-1-1110000000000000000i3−i3−i3i3−i3i3i3−i30000
χ412222-2-2-1-2-2-2-222-2-2-1-1-122112i2i2i2i−2i−2i−2i−2i11-1-1111100000000-1-1−i−i−i−iiiii0000000000002-22i−2i-1-111−i−iii0000
χ422222-2-2-1-2-2-2-222-2-2-1-1-122112i2i2i2i−2i−2i−2i−2i11-1-1111100000000-1-1−i−i−i−iiiii000000000000-22−2i2i11-1-1ii−i−i0000
χ432222-2-2-1-2-2-2-222-2-2-1-1-12211−2i−2i−2i−2i2i2i2i2i11-1-1111100000000-1-1iiii−i−i−i−i0000000000002-2−2i2i-1-111ii−i−i0000
χ442222-2-2-1-2-2-2-222-2-2-1-1-12211−2i−2i−2i−2i2i2i2i2i11-1-1111100000000-1-1iiii−i−i−i−i000000000000-222i−2i11-1-1−i−iii0000
χ4522-2-20022i−2i002-22i−2i-22-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2-2002i−2i000022-2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i2i−2i000000000000000000
χ4622-2-20022i−2i002-22i−2i-22-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2-2002i−2i0000-2-222001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i000000000000000000
χ4722-2-20022i−2i002-22i−2i-22-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2-2002i−2i000022-2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i2i−2i000000000000000000
χ4822-2-20022i−2i002-22i−2i-22-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2-2002i−2i0000-2-22200−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i000000000000000000
χ4922-2-20022i−2i00-22−2i2i-22-200001−i−1+i−1+i1−i−1−i1+i1+i−1−i2i−2i-2200−2i2i2i2i−2i−2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i002-20000000000000000
χ5022-2-20022i−2i00-22−2i2i-22-200001−i−1+i−1+i1−i−1−i1+i1+i−1−i2i−2i-2200−2i2i−2i−2i2i2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00-220000000000000000
χ5122-2-20022i−2i00-22−2i2i-22-20000−1+i1−i1−i−1+i1+i−1−i−1−i1+i2i−2i-2200−2i2i2i2i−2i−2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i002-20000000000000000
χ5222-2-20022i−2i00-22−2i2i-22-20000−1+i1−i1−i−1+i1+i−1−i−1−i1+i2i−2i-2200−2i2i−2i−2i2i2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00-220000000000000000
χ5322-2-2002−2i2i002-2−2i2i-22-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i2-200−2i2i000022-2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−2i2i000000000000000000
χ5422-2-2002−2i2i002-2−2i2i-22-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i2-200−2i2i0000-2-222001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i000000000000000000
χ5522-2-2002−2i2i002-2−2i2i-22-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i2-200−2i2i000022-2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2i2i000000000000000000
χ5622-2-2002−2i2i002-2−2i2i-22-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i2-200−2i2i0000-2-22200−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i000000000000000000
χ5722-2-2002−2i2i00-222i−2i-22-200001+i−1−i−1−i1+i−1+i1−i1−i−1+i−2i2i-22002i−2i2i2i−2i−2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00-220000000000000000
χ5822-2-2002−2i2i00-222i−2i-22-200001+i−1−i−1−i1+i−1+i1−i1−i−1+i−2i2i-22002i−2i−2i−2i2i2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i002-20000000000000000
χ5922-2-2002−2i2i00-222i−2i-22-20000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2i2i-22002i−2i2i2i−2i−2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00-220000000000000000
χ6022-2-2002−2i2i00-222i−2i-22-20000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2i2i-22002i−2i−2i−2i2i2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i002-20000000000000000
χ61444444-2-4-44444-4-4-2-2-2-4-4-2-20000000022-2-2-2-2220000000022000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-444-2-2-24-4-2-200000000222222-2-2000000002-2000000000000000000000000000000000000
χ634444-4-4-24444-4-4-4-4-2-2-24-42200000000-2-222-2-222000000002-2000000000000000000000000000000000000
χ644444-4-4-244-4-44444-2-2-2-4-42200000000-2-2-2-222-2-20000000022000000000000000000000000000000000000
χ6544-4-400-24i−4i004-44i−4i2-2200002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i−2i2i-2200−2i2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000000
χ6644-4-400-24i−4i004-44i−4i2-220000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i−2i2i-2200−2i2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000000
χ6744-4-400-24i−4i00-44−4i4i2-2200002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i−2i2i2-2002i−2i0000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000000000000000
χ6844-4-400-24i−4i00-44−4i4i2-220000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i−2i2i2-2002i−2i00000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000000000000000
χ6944-4-400-2−4i4i004-4−4i4i2-2200002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i2i−2i-22002i−2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000000
χ7044-4-400-2−4i4i004-4−4i4i2-220000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i2i−2i-22002i−2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000000
χ7144-4-400-2−4i4i00-444i−4i2-2200002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i2i−2i2-200−2i2i0000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000000000000000
χ7244-4-400-2−4i4i00-444i−4i2-220000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i2i−2i2-200−2i2i00000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000000000000000
χ734-44-4004004i−4i0000-4-4400000000000000004i−4i0022−2222−22−2i22i2−2i22i200000000000000000000000000000000000000
χ744-44-4004004i−4i0000-4-4400000000000000004i−4i00−2222−22222i2−2i22i2−2i200000000000000000000000000000000000000
χ754-44-400400−4i4i0000-4-440000000000000000−4i4i0022−2222−222i2−2i22i2−2i200000000000000000000000000000000000000
χ764-44-400400−4i4i0000-4-440000000000000000−4i4i00−2222−2222−2i22i2−2i22i200000000000000000000000000000000000000
χ774-4-444-44000000004-4-4004-40000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ784-4-444-44000000004-4-4004-400000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ794-4-44-444000000004-4-400-440000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ804-4-44-444000000004-4-400-4400000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ818-88-800-4008i−8i000044-40000000000000000−4i4i000000000000000000000000000000000000000000000000
χ828-88-800-400−8i8i000044-400000000000000004i−4i000000000000000000000000000000000000000000000000
χ838-8-888-8-400000000-44400-4400000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-400000000-444004-400000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).