Finite Group Databasebeta

← Group #10692793

Character table — Group #10692793

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212161616161616161616161616242424242424242424244848
order1222344444466624446688881212121212121212881212242424242424242488882266668824242424224488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ711111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1
χ811111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ911111-1-1-1-1-1-1111-1111-1-1ii−i−i11-1-1-1-1-1-1i−i11iiii−i−i−i−iii−i−i1-111-1-1i−iii−i−i1-11-1i−i11-1-1i−i
χ1011111-1-1-1-1-1-1111-1111-1-1ii−i−i11-1-1-1-1-1-1i−i11iiii−i−i−i−iii−i−i-11-1-111−ii−i−iii1-11-1i−i-1-111−ii
χ1111111-1-1-1-1-1-1111-1111-1-1ii−i−i11-1-1-1-1-1-1i−i11iiii−i−i−i−i−i−iii1-111-1-1i−iii−i−i-11-11−ii-1-111−ii
χ1211111-1-1-1-1-1-1111-1111-1-1ii−i−i11-1-1-1-1-1-1i−i11iiii−i−i−i−i−i−iii-11-1-111−ii−i−iii-11-11−ii11-1-1i−i
χ1311111-1-1-1-1-1-1111-1111-1-1−i−iii11-1-1-1-1-1-1−ii11−i−i−i−iiiiiii−i−i1-111-1-1−ii−i−iii-11-11i−i-1-111i−i
χ1411111-1-1-1-1-1-1111-1111-1-1−i−iii11-1-1-1-1-1-1−ii11−i−i−i−iiiiiii−i−i-11-1-111i−iii−i−i-11-11i−i11-1-1−ii
χ1511111-1-1-1-1-1-1111-1111-1-1−i−iii11-1-1-1-1-1-1−ii11−i−i−i−iiiii−i−iii1-111-1-1−ii−i−iii1-11-1−ii11-1-1−ii
χ1611111-1-1-1-1-1-1111-1111-1-1−i−iii11-1-1-1-1-1-1−ii11−i−i−i−iiiii−i−iii-11-1-111i−iii−i−i1-11-1−ii-1-111i−i
χ1722222222-2-22222-2-2-22-2-20000-2-2222-2-22002-200000000000000000000000022-2-200000000
χ1822222222-2-22222-2-2-22-2-20000-2-2222-2-22002-2000000000000000000000000-2-22200000000
χ19222222-2222-2222-22-2-2-2-22222-2-22-2-2222-2-2-2222-2-222-2-20000000000000000000000000000
χ20222222-2222-2222-22-2-2-2-2-2-2-2-2-2-22-2-222222-22-2-222-2-2220000000000000000000000000000
χ21222222-22-2-2-22222-22-2220000222-2-2-2-2200-2-2000000002i2i−2i−2i0000000000000000−2i2i000000
χ22222222-22-2-2-22222-22-2220000222-2-2-2-2200-2-200000000−2i−2i2i2i00000000000000002i−2i000000
χ2322222-22-2222222-2-22-2-2-2000022-22222-200-2-20000000022220000000000000000-2-2000000
χ2422222-22-2222222-2-22-2-2-2000022-22222-200-2-200000000-2-2-2-2000000000000000022000000
χ2522222-22-2-2-2222222-2-2222i2i−2i−2i-2-2-222-2-2-2−2i2i-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ2622222-22-2-2-2222222-2-222−2i−2i2i2i-2-2-222-2-2-22i−2i-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ2722222-2-2-222-22222-2-22220000-2-2-2-2-222-2002-20000000000000000000000002-2-2200000000
χ2822222-2-2-222-22222-2-22220000-2-2-2-2-222-2002-2000000000000000000000000-222-200000000
χ292222-1222222-1-1-12222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000022-1-1-1-122-1-1-1-1000000000000
χ302222-1222222-1-1-12222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-21111-2-21111000000000000
χ312222-1222222-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-111111111000022-1-1-1-1-2-21111000000000000
χ322222-1222222-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2111122-1-1-1-1000000000000
χ332222-12-2222-2-1-1-1-22-2-211222211-111-1-1-1-2-21-1-1-111-1-111000000−i3i3−i3i300−i3i3−i3i3000000000000
χ342222-12-2222-2-1-1-1-22-2-211222211-111-1-1-1-2-21-1-1-111-1-111000000i3−i3i3−i300i3−i3i3−i3000000000000
χ352222-12-2222-2-1-1-1-22-2-211-2-2-2-211-111-1-1-1221-111-1-111-1-1000000−i3i3−i3i300i3−i3i3−i3000000000000
χ362222-12-2222-2-1-1-1-22-2-211-2-2-2-211-111-1-1-1221-111-1-111-1-1000000i3−i3i3−i300−i3i3−i3i3000000000000
χ372222-1-22-2-2-22-1-1-122-2-2-1-12i2i−2i−2i111-1-1111−2i2i1-1−i−iiiii−i−i000000−i3i3i3−i3003−3−33000000000000
χ382222-1-22-2-2-22-1-1-122-2-2-1-12i2i−2i−2i111-1-1111−2i2i1-1−i−iiiii−i−i000000i3−i3−i3i300−333−3000000000000
χ392222-1-22-2-2-22-1-1-122-2-2-1-1−2i−2i2i2i111-1-11112i−2i1-1ii−i−i−i−iii000000−i3i3i3−i300−333−3000000000000
χ402222-1-22-2-2-22-1-1-122-2-2-1-1−2i−2i2i2i111-1-11112i−2i1-1ii−i−i−i−iii000000i3−i3−i3i3003−3−33000000000000
χ412222-1-2-2-2-2-2-2-1-1-1-2222112i2i−2i−2i-1-11111112i−2i-1-1−i−i−i−iiiii00002-2-1-1112i−2i−i−iii000000000000
χ422222-1-2-2-2-2-2-2-1-1-1-2222112i2i−2i−2i-1-11111112i−2i-1-1−i−i−i−iiiii0000-2211-1-1−2i2iii−i−i000000000000
χ432222-1-2-2-2-2-2-2-1-1-1-222211−2i−2i2i2i-1-1111111−2i2i-1-1iiii−i−i−i−i00002-2-1-111−2i2iii−i−i000000000000
χ442222-1-2-2-2-2-2-2-1-1-1-222211−2i−2i2i2i-1-1111111−2i2i-1-1iiii−i−i−i−i0000-2211-1-12i−2i−i−iii000000000000
χ454444-2444-4-44-2-2-2-4-4-4422000022-2-2-222-200-22000000000000000000000000000000000000
χ464444-24-44-4-4-4-2-2-24-44-4-2-20000-2-2-22222-20022000000000000000000000000000000000000
χ474444-2-44-4444-2-2-2-4-44-4220000-2-22-2-2-2-220022000000000000000000000000000000000000
χ484444-2-4-4-444-4-2-2-24-4-44-2-2000022222-2-2200-22000000000000000000000000000000000000
χ4944-4-4404000-44-4-400000000000004-4000000000000000−2i22i2−2i22i2000000000000000000000000
χ5044-4-4404000-44-4-400000000000004-40000000000000002i2−2i22i2−2i2000000000000000000000000
χ5144-4-440-400044-4-40000000000000-4400000000000000022−22−2222000000000000000000000000
χ5244-4-440-400044-4-40000000000000-44000000000000000−222222−22000000000000000000000000
χ534-44-4440-4000-44-4000000−2i22i2−2i22i20040000-40000−2i22i200−2i22i2000000000000000000000000000000
χ544-44-4440-4000-44-40000002i2−2i22i2−2i20040000-400002i2−2i2002i2−2i2000000000000000000000000000000
χ554-44-44-404000-44-400000022−22−222200-400004000022−2200−2222000000000000000000000000000000
χ564-44-44-404000-44-4000000−222222−2200-4000040000−22220022−22000000000000000000000000000000
χ574-44-4-240-40002-220000−2i32i3−2i22i2−2i22i2−2i32i3-2000020000i2−i26−6i2−i26−60000000000000000000000000000
χ584-44-4-240-40002-220000−2i32i32i2−2i22i2−2i2−2i32i3-2000020000−i2i2−66−i2i2−660000000000000000000000000000
χ594-44-4-240-40002-2200002i3−2i3−2i22i2−2i22i22i3−2i3-2000020000i2−i2−66i2−i2−660000000000000000000000000000
χ604-44-4-240-40002-2200002i3−2i32i2−2i22i2−2i22i3−2i3-2000020000−i2i26−6−i2i26−60000000000000000000000000000
χ614-44-4-2-4040002-220000−2i32i322−22−22222i3−2i320000-20000−22−i6i62−2i6−i60000000000000000000000000000
χ624-44-4-2-4040002-220000−2i32i3−222222−222i3−2i320000-200002−2i6−i6−22−i6i60000000000000000000000000000
χ634-44-4-2-4040002-2200002i3−2i322−22−2222−2i32i320000-20000−22i6−i62−2−i6i60000000000000000000000000000
χ644-44-4-2-4040002-2200002i3−2i3−222222−22−2i32i320000-200002−2−i6i6−22i6−i60000000000000000000000000000
χ654-4-4440004-40-4-440000000000000004-4000000000000000000000000000000000002-22-200
χ664-4-4440004-40-4-440000000000000004-400000000000000000000000000000000000-22-2200
χ674-4-444000-440-4-44000000000000000-44000000000000000000000000000000000002-2-2200
χ684-4-444000-440-4-44000000000000000-4400000000000000000000000000000000000-222-200
χ6988-8-8-408000-8-4440000000000000-440000000000000000000000000000000000000000000
χ7088-8-8-40-80008-44400000000000004-40000000000000000000000000000000000000000000
χ718-8-88-40008-8044-4000000000000000-4400000000000000000000000000000000000000000
χ728-8-88-4000-88044-40000000000000004-400000000000000000000000000000000000000000

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