Finite Group Databasebeta

← Group #10691868

Character table — Group #10691868

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888816161616161616161616161624242424242424242424242424242424
order122222344446666666444488881212121288121212122424242424242424444412121212121212124444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1111-1-1-1-111-1-111-11-1ii−i−i11-1-1i−i11-1-1iiii−i−i−i−i1-1i−iii−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i
χ101111-1-1111-1-1-1-111-1-111-11-1ii−i−i11-1-1i−i11-1-1iiii−i−i−i−i1-1i−iii−i−i11-1-1-1-111−i−iii-1-111−i−iii
χ111111-1-1111-1-1-1-111-1-111-11-1ii−i−i11-1-1i−i11-1-1iiii−i−i−i−i-11−ii−i−iii-1-11111-1-1ii−i−i-1-111−i−iii
χ121111-1-1111-1-1-1-111-1-111-11-1ii−i−i11-1-1i−i11-1-1iiii−i−i−i−i-11−ii−i−iii-1-111-1-111−i−iii11-1-1ii−i−i
χ131111-1-1111-1-1-1-111-1-111-11-1−i−iii11-1-1−ii11-1-1−i−i−i−iiiii1-1−ii−i−iii11-1-111-1-1−i−iii11-1-1−i−iii
χ141111-1-1111-1-1-1-111-1-111-11-1−i−iii11-1-1−ii11-1-1−i−i−i−iiiii1-1−ii−i−iii11-1-1-1-111ii−i−i-1-111ii−i−i
χ151111-1-1111-1-1-1-111-1-111-11-1−i−iii11-1-1−ii11-1-1−i−i−i−iiiii-11i−iii−i−i-1-11111-1-1−i−iii-1-111ii−i−i
χ161111-1-1111-1-1-1-111-1-111-11-1−i−iii11-1-1−ii11-1-1−i−i−i−iiiii-11i−iii−i−i-1-111-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222-2-2-2-222222222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2222222222-2-20000-2-2-2-2002-22-20000000000000000000000002i−2i2i−2i00000000
χ202222222-2-2-2-2222222222-2-20000-2-2-2-2002-22-2000000000000000000000000−2i2i−2i2i00000000
χ212222222-2-2-2-22222222-2-2220000-2-2-2-200-22-22000000000000000000002-22-2000000000000
χ222222222-2-2-2-22222222-2-2220000-2-2-2-200-22-2200000000000000000000-22-22000000000000
χ23222222-12222-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ24222222-12222-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ25222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-2-2-1-1-1-11111111122-2-21111-1-1-1-10000000000000000
χ26222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-2-2-1-1-1-111111111-2-222-1-1-1-111110000000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-2-21111-1-111-1-1110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-2-21111-1-111-1-1110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ29222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122111111-1-111-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ30222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122111111-1-111-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ312222-2-2222-2-2-2-222-2-22-22-222i2i−2i−2i22-2-2−2i2i-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ322222-2-2222-2-2-2-222-2-22-22-22−2i−2i2i2i22-2-22i−2i-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ332222-2-22-2-222-2-222-2-222-2-220000-2-222002-2-220000000000000000000000002-2-2200000000
χ342222-2-22-2-222-2-222-2-222-2-220000-2-222002-2-22000000000000000000000000-222-200000000
χ352222-2-22-2-222-2-222-2-22-222-20000-2-22200-222-2000000000000000000002-2-22000000000000
χ362222-2-22-2-222-2-222-2-22-222-20000-2-22200-222-200000000000000000000-222-2000000000000
χ372222-2-2-122-2-211-1-111-12-22-22i2i−2i−2i-1-1112i−2i-1-111−i−i−i−iiiii2-22i−2i−i−iii-1-1110000000000000000
χ382222-2-2-122-2-211-1-111-12-22-22i2i−2i−2i-1-1112i−2i-1-111−i−i−i−iiiii-22−2i2iii−i−i11-1-10000000000000000
χ392222-2-2-122-2-211-1-111-12-22-2−2i−2i2i2i-1-111−2i2i-1-111iiii−i−i−i−i2-2−2i2iii−i−i-1-1110000000000000000
χ402222-2-2-122-2-211-1-111-12-22-2−2i−2i2i2i-1-111−2i2i-1-111iiii−i−i−i−i-222i−2i−i−iii11-1-10000000000000000
χ412222-2-2-122-2-211-1-111-1-22-222i2i−2i−2i-1-111−2i2i11-1-1−i−iiiii−i−i00003−3−33−i3i3i3−i30000000000000000
χ422222-2-2-122-2-211-1-111-1-22-222i2i−2i−2i-1-111−2i2i11-1-1−i−iiiii−i−i0000−333−3i3−i3−i3i30000000000000000
χ432222-2-2-122-2-211-1-111-1-22-22−2i−2i2i2i-1-1112i−2i11-1-1ii−i−i−i−iii00003−3−33i3−i3−i3i30000000000000000
χ442222-2-2-122-2-211-1-111-1-22-22−2i−2i2i2i-1-1112i−2i11-1-1ii−i−i−i−iii0000−333−3−i3i3i3−i30000000000000000
χ4522-2-22-222-2-2222-2-2-2-2200002i−2i2i−2i2-22-20000002i−2i002i−2i0000000000000000000000−i2i2−i2i22−22−2
χ4622-2-22-222-2-2222-2-2-2-2200002i−2i2i−2i2-22-20000002i−2i002i−2i0000000000000000000000i2−i2i2−i2−22−22
χ4722-2-22-222-2-2222-2-2-2-220000−2i2i−2i2i2-22-2000000−2i2i00−2i2i0000000000000000000000−i2i2−i2i2−22−22
χ4822-2-22-222-2-2222-2-2-2-220000−2i2i−2i2i2-22-2000000−2i2i00−2i2i0000000000000000000000i2−i2i2−i22−22−2
χ4922-2-2-2222-22-2-2-2-2-222200002-2-222-2-220000002-200-220000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ5022-2-2-2222-22-2-2-2-2-222200002-2-222-2-220000002-200-220000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ5122-2-2-2222-22-2-2-2-2-22220000-222-22-2-22000000-22002-20000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ5222-2-2-2222-22-2-2-2-2-22220000-222-22-2-22000000-22002-20000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ53444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000222200-22-22000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44400002222002-22-2000000000000000000000000000000000000
χ554444-4-4-2-4-44422-2-222-24-4-44000022-2-200-222-2000000000000000000000000000000000000
χ564444-4-4-2-4-44422-2-222-2-444-4000022-2-2002-2-22000000000000000000000000000000000000
χ5744-4-44-44-444-444-4-4-4-4400000000-44-44000000000000000000000000000000000000000000
χ5844-4-44-4-24-4-44-2-22222-200004i−4i4i−4i-22-22000000−2i2i00−2i2i000000000000000000000000000000
χ5944-4-44-4-24-4-44-2-22222-20000−4i4i−4i4i-22-220000002i−2i002i−2i000000000000000000000000000000
χ6044-4-44-4-2-444-4-2-22222-2000000002-22-20000000023−230023−230000000000000000000000000000
χ6144-4-44-4-2-444-4-2-22222-2000000002-22-200000000−232300−23230000000000000000000000000000
χ6244-4-4-444-44-44-4-4-4-444400000000-444-4000000000000000000000000000000000000000000
χ6344-4-4-44-24-44-42222-2-2-200004-4-44-222-2000000-22002-2000000000000000000000000000000
χ6444-4-4-44-24-44-42222-2-2-20000-444-4-222-20000002-200-22000000000000000000000000000000
χ6544-4-4-44-2-44-442222-2-2-2000000002-2-2200000000−2i32i3002i3−2i30000000000000000000000000000
χ6644-4-4-44-2-44-442222-2-2-2000000002-2-22000000002i3−2i300−2i32i30000000000000000000000000000
χ678-88-80080000008-800-8000000000000000000000000000000000000000000000000000000
χ688-88-800-40000−4i34i3-44−4i34i34000000000000000000000000000000000000000000000000000000
χ698-88-800-400004i3−4i3-444i3−4i34000000000000000000000000000000000000000000000000000000
χ708-8-88008000000-8800-8000000000000000000000000000000000000000000000000000000
χ718-8-8800-40000−4i34i34-44i3−4i34000000000000000000000000000000000000000000000000000000
χ728-8-8800-400004i3−4i34-4−4i34i34000000000000000000000000000000000000000000000000000000

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