Finite Group Databasebeta

← Group #10693270

Character table — Group #10693270

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881616161616161616161616162424242424242424242424244848
order122234444666244448888121212121212121212126881224242424242424248888242424242424242444444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ511111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-111
χ811111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1
χ911111-1-1-1-11111-11-11ii−i−i11-1-111-1-1-1-11i−i-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1111-1-1-1ii−i−ii−i
χ1011111-1-1-1-11111-11-11ii−i−i11-1-111-1-1-1-11i−i-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i-11-1-1-1111−i−iii−ii
χ1111111-1-1-1-11111-11-11ii−i−i11-1-111-1-1-1-11i−i-1iiii−i−i−i−i-11−ii-1-111−i−iii1-1-1-11-111ii−i−i−ii
χ1211111-1-1-1-11111-11-11ii−i−i11-1-111-1-1-1-11i−i-1iiii−i−i−i−i-11−ii-1-111−i−iii-1111-11-1-1−i−iiii−i
χ1311111-1-1-1-11111-11-11−i−iii11-1-111-1-1-1-11−ii-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1111-1-1-1−i−iii−ii
χ1411111-1-1-1-11111-11-11−i−iii11-1-111-1-1-1-11−ii-1−i−i−i−iiiii1-1−ii11-1-1−i−iii-11-1-1-1111ii−i−ii−i
χ1511111-1-1-1-11111-11-11−i−iii11-1-111-1-1-1-11−ii-1−i−i−i−iiiii-11i−i-1-111ii−i−i1-1-1-11-111−i−iiii−i
χ1611111-1-1-1-11111-11-11−i−iii11-1-111-1-1-1-11−ii-1−i−i−i−iiiii-11i−i-1-111ii−i−i-1111-11-1-1ii−i−i−ii
χ17222222222222-2-22-2-222222222-2-222-2-2-2-2-2-222-2-222-2-200000000000000000000000000
χ18222222222222-2-22-2-2-2-2-2-22222-2-222-2-2-222-2-2-222-2-22200000000000000000000000000
χ19222222-2-2222222-2-2-20000-2-222-2-2-2-2-2-2200200000000000000000000000000002i−2i2i−2i00
χ20222222-2-2222222-2-2-20000-2-222-2-2-2-2-2-220020000000000000000000000000000−2i2i−2i2i00
χ21222222-2-22222-2-2-2220000-2-22222-2-222-200-2000000000000000000002200-2-200000000
χ22222222-2-22222-2-2-2220000-2-22222-2-222-200-200000000000000000000-2-2002200000000
χ2322222-222-22222-2-22-20000-2-2-2-2-2-22222200-200000000000000000000000000002-2-2200
χ2422222-222-22222-2-22-20000-2-2-2-2-2-22222200-20000000000000000000000000000-222-200
χ2522222-222-2222-22-2-220000-2-2-2-22222-2-2-2002000000000000000000002-200-2200000000
χ2622222-222-2222-22-2-220000-2-2-2-22222-2-2-200200000000000000000000-22002-200000000
χ2722222-2-2-2-2222-2222-22i2i−2i−2i22-2-2-2-2-2-222-2−2i2i22i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ2822222-2-2-2-2222-2222-2−2i−2i2i2i22-2-2-2-2-2-222-22i−2i2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ292222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ302222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ312222-12222-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-2-2-11111111122-2-2-1-1-1-1111100000000000000
χ322222-12222-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-2-2-111111111-2-2221111-1-1-1-100000000000000
χ332222-12222-1-1-1-2-22-2-22222-1-1-1-111-1-1111-2-21-1-111-1-11100003−33−33−33−300000000000000
χ342222-12222-1-1-1-2-22-2-22222-1-1-1-111-1-1111-2-21-1-111-1-1110000−33−33−33−3300000000000000
χ352222-12222-1-1-1-2-22-2-2-2-2-2-2-1-1-1-111-1-111122111-1-111-1-100003−33−3−33−3300000000000000
χ362222-12222-1-1-1-2-22-2-2-2-2-2-2-1-1-1-111-1-111122111-1-111-1-10000−33−333−33−300000000000000
χ372222-1-2-2-2-2-1-1-12-22-222i2i−2i−2i-1-111-1-11111-12i−2i1−i−i−i−iiiii2-22i−2i-1-111−i−iii00000000000000
χ382222-1-2-2-2-2-1-1-12-22-222i2i−2i−2i-1-111-1-11111-12i−2i1−i−i−i−iiiii-22−2i2i11-1-1ii−i−i00000000000000
χ392222-1-2-2-2-2-1-1-12-22-22−2i−2i2i2i-1-111-1-11111-1−2i2i1iiii−i−i−i−i2-2−2i2i-1-111ii−i−i00000000000000
χ402222-1-2-2-2-2-1-1-12-22-22−2i−2i2i2i-1-111-1-11111-1−2i2i1iiii−i−i−i−i-222i−2i11-1-1−i−iii00000000000000
χ412222-1-2-2-2-2-1-1-1-2222-22i2i−2i−2i-1-1111111-1-11−2i2i-1−i−iiiii−i−i00003−3−33i3−i3−i3i300000000000000
χ422222-1-2-2-2-2-1-1-1-2222-22i2i−2i−2i-1-1111111-1-11−2i2i-1−i−iiiii−i−i0000−333−3−i3i3i3−i300000000000000
χ432222-1-2-2-2-2-1-1-1-2222-2−2i−2i2i2i-1-1111111-1-112i−2i-1ii−i−i−i−iii00003−3−33−i3i3i3−i300000000000000
χ442222-1-2-2-2-2-1-1-1-2222-2−2i−2i2i2i-1-1111111-1-112i−2i-1ii−i−i−i−iii0000−333−3i3−i3−i3i300000000000000
χ454444-24-4-44-2-2-244-4-4-4000022-2-2222222-200-20000000000000000000000000000000000
χ464444-24-4-44-2-2-2-4-4-444000022-2-2-2-222-2-220020000000000000000000000000000000000
χ474444-2-444-4-2-2-24-4-44-40000222222-2-2-2-2-20020000000000000000000000000000000000
χ484444-2-444-4-2-2-2-44-4-4400002222-2-2-2-222200-20000000000000000000000000000000000
χ4944-4-44400-44-4-40000022−2222−22004-4000000000022−220022−220000000000000000000000000000
χ5044-4-44400-44-4-400000−2222−2222004-40000000000−222200−22220000000000000000000000000000
χ5144-4-44-40044-4-400000−2i22i22i2−2i200-440000000000−2i22i2002i2−2i20000000000000000000000000000
χ5244-4-44-40044-4-4000002i2−2i2−2i22i200-4400000000002i2−2i200−2i22i20000000000000000000000000000
χ5344-4-4-2400-4-2220000022−2222−2200-2223−230023−230000−226−6−226−600000000000000000000000000
χ5444-4-4-2400-4-2220000022−2222−2200-22−232300−23230000−22−66−22−6600000000000000000000000000
χ5544-4-4-2400-4-22200000−2222−222200-2223−230023−2300002−2−662−2−6600000000000000000000000000
χ5644-4-4-2400-4-22200000−2222−222200-22−232300−232300002−26−62−26−600000000000000000000000000
χ5744-4-4-2-4004-22200000−2i22i22i2−2i2002-223−2300−23230000i2−i2−i6i6−i2i2i6−i600000000000000000000000000
χ5844-4-4-2-4004-22200000−2i22i22i2−2i2002-2−23230023−230000i2−i2i6−i6−i2i2−i6i600000000000000000000000000
χ5944-4-4-2-4004-222000002i2−2i2−2i22i2002-223−2300−23230000−i2i2i6−i6i2−i2−i6i600000000000000000000000000
χ6044-4-4-2-4004-222000002i2−2i2−2i22i2002-2−23230023−230000−i2i2−i6i6i2−i2i6−i600000000000000000000000000
χ614-4-44404i−4i0-44-40000000000000004i−4i00000000000000000000000000002i−2i002-2000000
χ624-4-44404i−4i0-44-40000000000000004i−4i0000000000000000000000000000−2i2i00-22000000
χ634-4-4440−4i4i0-44-4000000000000000−4i4i00000000000000000000000000002i−2i00-22000000
χ644-4-4440−4i4i0-44-4000000000000000−4i4i0000000000000000000000000000−2i2i002-2000000
χ658-88-880000-8-88000000000000000000000000000000000000000000000000000000000
χ668-88-8-4000044-400000000043−430000000000000000000000000000000000000000000000
χ678-88-8-4000044-4000000000−43430000000000000000000000000000000000000000000000
χ688-8-88-408i−8i04-44000000000000000−4i4i0000000000000000000000000000000000000000
χ698-8-88-40−8i8i04-440000000000000004i−4i0000000000000000000000000000000000000000

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