Finite Group Databasebeta

← Group #10691744

Character table — Group #10691744

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order12222222223446664446666661212121222448888121224242424242424244444444444661212121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1
χ9111111-1-1-1-11-1-11111-1111-1-1-1-1-1-1-1-11-11-1ii−i−i11iiii−i−i−i−iii−i−iii−i−ii−i1-11-1ii−i−ii−ii−i11-1-11-1
χ10111111-1-1-1-11-1-11111-1111-1-1-1-1-1-1-1-11-11-1ii−i−i11iiii−i−i−i−i−i−iii−i−iiii−i1-11-1ii−i−i−ii−ii-1-111-11
χ11111111-1-1-1-11-1-11111-1111-1-1-1-1-1-1-1-11-11-1−i−iii11−i−i−i−iiiiiii−i−iii−i−i−ii1-11-1−i−iiii−ii−i-1-111-11
χ12111111-1-1-1-11-1-11111-1111-1-1-1-1-1-1-1-11-11-1−i−iii11−i−i−i−iiiii−i−iii−i−iii−ii1-11-1−i−iii−ii−ii11-1-11-1
χ13111111-1-1-1-11-1-11111-1111-1-1-1-1-1-1-1-1-11-11ii−i−i11iiii−i−i−i−iii−i−i−i−iii−ii-11-11−i−iiii−i−ii11-1-1-11
χ14111111-1-1-1-11-1-11111-1111-1-1-1-1-1-1-1-1-11-11ii−i−i11iiii−i−i−i−i−i−iiiii−i−i−ii-11-11−i−iii−iii−i-1-1111-1
χ15111111-1-1-1-11-1-11111-1111-1-1-1-1-1-1-1-1-11-11−i−iii11−i−i−i−iiiiiii−i−i−i−iiii−i-11-11ii−i−ii−i−ii-1-1111-1
χ16111111-1-1-1-11-1-11111-1111-1-1-1-1-1-1-1-1-11-11−i−iii11−i−i−i−iiiii−i−iiiii−i−ii−i-11-11ii−i−i−iii−i11-1-1-11
χ1722222222222-2-2222-2-2-2222222-2-2-2-200000000-2-200000000222200000000000000-2-200000000
χ1822222222222-2-2222-2-2-2222222-2-2-2-200000000-2-200000000-2-2-2-2000000000000002200000000
χ192222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ202222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-2-1-1-1-111110000000000
χ212222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ222222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111100000000221111-1-1-1-10000000000
χ23222222-2-2-2-2222222-22-222-2-2-2-2222200000000-2-2000000002i2i−2i−2i00000000000000−2i2i00000000
χ24222222-2-2-2-2222222-22-222-2-2-2-2222200000000-2-200000000−2i−2i2i2i000000000000002i−2i00000000
χ25222222-2-2-2-2-1-2-2-1-1-12-22-1-1111111112-22-22i2i−2i−2i-1-1−i−i−i−iiiii000000002i−2i-11-11−i−iii0000000000
χ26222222-2-2-2-2-1-2-2-1-1-12-22-1-1111111112-22-2−2i−2i2i2i-1-1iiii−i−i−i−i00000000−2i2i-11-11ii−i−i0000000000
χ27222222-2-2-2-2-1-2-2-1-1-12-22-1-111111111-22-222i2i−2i−2i-1-1−i−i−i−iiiii00000000−2i2i1-11-1ii−i−i0000000000
χ28222222-2-2-2-2-1-2-2-1-1-12-22-1-111111111-22-22−2i−2i2i2i-1-1iiii−i−i−i−i000000002i−2i1-11-1−i−iii0000000000
χ292222-2-222-2-2222222-2-22-2-22-2-22-2-2222-2-2200002-20000000000000000002-2-2200000000000000
χ302222-2-222-2-2222222-2-22-2-22-2-22-2-222-222-200002-2000000000000000000-222-200000000000000
χ312222-2-222-2-22-2-222222-2-2-22-2-2222-2-200000000-220000000000002i2i−2i−2i000000000000−2i2i000000
χ322222-2-222-2-22-2-222222-2-2-22-2-2222-2-200000000-22000000000000−2i−2i2i2i0000000000002i−2i000000
χ332222-2-222-2-2-122-1-1-1-2-2211-111-111-1-12-2-220000-11−i3−i3i3i3−i3−i3i3i30000000000-111-1−i3i3−i3i30000000000
χ342222-2-222-2-2-122-1-1-1-2-2211-111-111-1-12-2-220000-11i3i3−i3−i3i3i3−i3−i30000000000-111-1i3−i3i3−i30000000000
χ352222-2-222-2-2-122-1-1-1-2-2211-111-111-1-1-222-20000-11−i3−i3i3i3−i3−i3i3i300000000001-1-11i3−i3i3−i30000000000
χ362222-2-222-2-2-122-1-1-1-2-2211-111-111-1-1-222-20000-11i3i3−i3−i3i3i3−i3−i300000000001-1-11−i3i3−i3i30000000000
χ372222-2-2-2-2222222222-2-2-2-2-222-2-2-22200000000-220000000000002222000000000000-2-2000000
χ382222-2-2-2-2222222222-2-2-2-2-222-2-2-22200000000-22000000000000-2-2-2-200000000000022000000
χ392222-2-2-2-2222-2-2222-222-2-2-222-222-2-222-2-200002-200000000000000000022-2-200000000000000
χ402222-2-2-2-2222-2-2222-222-2-2-222-222-2-2-2-22200002-2000000000000000000-2-22200000000000000
χ412222-2-2-2-222-1-2-2-1-1-1-222111-1-11-1-11122-2-20000-1133−3−3−3−3330000000000-1-1113−3−330000000000
χ422222-2-2-2-222-1-2-2-1-1-1-222111-1-11-1-11122-2-20000-11−3−33333−3−30000000000-1-111−333−30000000000
χ432222-2-2-2-222-1-2-2-1-1-1-222111-1-11-1-111-2-2220000-1133−3−3−3−333000000000011-1-1−333−30000000000
χ442222-2-2-2-222-1-2-2-1-1-1-222111-1-11-1-111-2-2220000-11−3−33333−3−3000000000011-1-13−3−330000000000
χ4522-2-22-22-2-22200-22-20002-222-2-200000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i22-22-2000000000000000000−i2i2−i2i200
χ4622-2-22-22-2-22200-22-20002-222-2-200000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2-22-22000000000000000000i2−i2i2−i200
χ4722-2-22-22-2-22200-22-20002-222-2-200000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i22-22-2000000000000000000i2−i2i2−i200
χ4822-2-22-22-2-22200-22-20002-222-2-200000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2-22-22000000000000000000−i2i2−i2i200
χ4922-2-22-2-222-2200-22-20002-2-2-222000000002−2−22002−22−2−22−222i−2i−2i2i000000000000000000−i2i2i2−i200
χ5022-2-22-2-222-2200-22-20002-2-2-222000000002−2−22002−22−2−22−22−2i2i2i−2i000000000000000000i2−i2−i2i200
χ5122-2-22-2-222-2200-22-20002-2-2-22200000000−222−200−22−222−22−22i−2i−2i2i000000000000000000i2−i2−i2i200
χ5222-2-22-2-222-2200-22-20002-2-2-22200000000−222−200−22−222−22−2−2i2i2i−2i000000000000000000−i2i2i2−i200
χ534444444444-2-4-4-2-2-2-4-4-4-2-2-2-2-2-222220000000022000000000000000000000000000000000000
χ54444444-4-4-4-4-244-2-2-2-44-4-2-22222-2-2-2-20000000022000000000000000000000000000000000000
χ554444-4-444-4-4-2-4-4-2-2-244-422-222-2-2-222000000002-2000000000000000000000000000000000000
χ564444-4-4-4-444-244-2-2-24-4-4222-2-2222-2-2000000002-2000000000000000000000000000000000000
χ5744-4-44-44-4-44-2002-22000-22-2-22200000000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ5844-4-44-44-4-44-2002-22000-22-2-222000000002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ5944-4-44-4-444-4-2002-22000-2222-2-20000000022−22−222200−22−222−22−20000000000000000000000000000
χ6044-4-44-4-444-4-2002-22000-2222-2-200000000−222222−22002−22−2−22−220000000000000000000000000000
χ6144-4-4-444-44-4400-44-4000-444-44-400000000000000000000000000000000000000000000000000
χ6244-4-4-444-44-4-2002-220002-2-22-22000000000000006−6−666−6−660000000000000000000000000000
χ6344-4-4-444-44-4-2002-220002-2-22-2200000000000000−666−6−666−60000000000000000000000000000
χ6444-4-4-44-44-44400-44-4000-44-44-4400000000000000000000000000000000000000000000000000
χ6544-4-4-44-44-44-2002-220002-22-22-200000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ6644-4-4-44-44-44-2002-220002-22-22-200000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ674-44-400000044i−4i4-4-4000000000004i−4i00000000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000
χ684-44-400000044i−4i4-4-4000000000004i−4i0000000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000
χ694-44-40000004−4i4i4-4-400000000000−4i4i00000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000
χ704-44-40000004−4i4i4-4-400000000000−4i4i0000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000
χ718-88-8000000-48i−8i-44400000000000−4i4i0000000000000000000000000000000000000000000000
χ728-88-8000000-4−8i8i-444000000000004i−4i0000000000000000000000000000000000000000000000
χ738-8-88000000800-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-88000000-40044-4000000000−4i34i3000000000000000000000000000000000000000000000000
χ758-8-88000000-40044-40000000004i3−4i3000000000000000000000000000000000000000000000000

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