Finite Group Databasebeta

← Group #10692965

Character table — Group #10692965

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order1222222222344666444666666121212128888121224242424242424244444121212121212121224444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ911111-1-11-1-11-1-111111-11-1-1-11-111-1-1ii−i−i1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-111-1-1ii−i−ii−i
χ1011111-1-11-1-11-1-111111-11-1-1-11-111-1-1ii−i−i1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i-1-111-1-111−i−iii−ii
χ1111111-1-11-1-11-1-111111-11-1-1-11-111-1-1ii−i−i1-1iiii−i−i−i−i-11−ii-1-111−i−iii11-1-1-1-111ii−i−i−ii
χ1211111-1-11-1-11-1-111111-11-1-1-11-111-1-1ii−i−i1-1iiii−i−i−i−i-11−ii-1-111−i−iii-1-11111-1-1−i−iiii−i
χ1311111-1-11-1-11-1-111111-11-1-1-11-111-1-1−i−iii1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-111-1-1−i−iii−ii
χ1411111-1-11-1-11-1-111111-11-1-1-11-111-1-1−i−iii1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii-1-111-1-111ii−i−ii−i
χ1511111-1-11-1-11-1-111111-11-1-1-11-111-1-1−i−iii1-1−i−i−i−iiiii-11i−i-1-111ii−i−i11-1-1-1-111−i−iiii−i
χ1611111-1-11-1-11-1-111111-11-1-1-11-111-1-1−i−iii1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-1-11111-1-1ii−i−i−ii
χ1722222222222-2-2222-2-2-2222222-2-2-2-20000-2-2000000000000000000002-22-20000000000
χ1822222222222-2-2222-2-2-2222222-2-2-2-20000-2-200000000000000000000-22-220000000000
χ192222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ202222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ212222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ222222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ2322222-2-22-2-2222222-2-222-2-2-22-2-2-2220000-22000000000000000000002-2-220000000000
χ2422222-2-22-2-2222222-2-222-2-2-22-2-2-2220000-2200000000000000000000-222-20000000000
χ2522222-2-22-2-2-1-2-2-1-1-122-2-1111-11-1-1112i2i−2i−2i-11−i−i−i−iiiii2-22i−2i-1-111−i−iii00000000000000
χ2622222-2-22-2-2-1-2-2-1-1-122-2-1111-11-1-1112i2i−2i−2i-11−i−i−i−iiiii-22−2i2i11-1-1ii−i−i00000000000000
χ2722222-2-22-2-2-1-2-2-1-1-122-2-1111-11-1-111−2i−2i2i2i-11iiii−i−i−i−i2-2−2i2i-1-111ii−i−i00000000000000
χ2822222-2-22-2-2-1-2-2-1-1-122-2-1111-11-1-111−2i−2i2i2i-11iiii−i−i−i−i-222i−2i11-1-1−i−iii00000000000000
χ292222-22-2-22-22222222-2-2-22-2-2-22-2-22200002-200000000000000000000000000002-22-200
χ302222-22-2-22-22222222-2-2-22-2-2-22-2-22200002-20000000000000000000000000000-22-2200
χ312222-22-2-22-22-2-2222-222-22-2-2-2222-2-22i−2i2i−2i-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ322222-22-2-22-22-2-2222-222-22-2-2-2222-2-2−2i2i−2i2i-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ332222-22-2-22-2-1-2-2-1-1-1-2221-1111-1-1-1112i−2i2i−2i1-1−i−iii−i−iii00003−33−3−i3i3−i3i300000000000000
χ342222-22-2-22-2-1-2-2-1-1-1-2221-1111-1-1-1112i−2i2i−2i1-1−i−iii−i−iii0000−33−33i3−i3i3−i300000000000000
χ352222-22-2-22-2-1-2-2-1-1-1-2221-1111-1-1-111−2i2i−2i2i1-1ii−i−iii−i−i00003−33−3i3−i3i3−i300000000000000
χ362222-22-2-22-2-1-2-2-1-1-1-2221-1111-1-1-111−2i2i−2i2i1-1ii−i−iii−i−i0000−33−33−i3i3−i3i300000000000000
χ372222-2-22-2-22222222-22-2-2-222-2-222222-2-22-2-222-2-2-2-22200000000000000000000000000
χ382222-2-22-2-22222222-22-2-2-222-2-22222-222-2-2-2-2-22222-2-200000000000000000000000000
χ392222-2-22-2-222-2-22222-22-2-222-2-2-2-2-2-200002200000000000000000000000000002i−2i−2i2i00
χ402222-2-22-2-222-2-22222-22-2-222-2-2-2-2-2-20000220000000000000000000000000000−2i2i2i−2i00
χ412222-2-22-2-22-122-1-1-1-22-211-1-111-1-1-1-12-2-2211-1-11111-1-100003−3−33−333−300000000000000
χ422222-2-22-2-22-122-1-1-1-22-211-1-111-1-1-1-12-2-2211-1-11111-1-10000−333−33−3−3300000000000000
χ432222-2-22-2-22-122-1-1-1-22-211-1-111-1-1-1-1-222-21111-1-1-1-11100003−3−333−3−3300000000000000
χ442222-2-22-2-22-122-1-1-1-22-211-1-111-1-1-1-1-222-21111-1-1-1-1110000−333−3−333−300000000000000
χ454444444444-2-4-4-2-2-2-4-4-4-2-2-2-2-2-222220000220000000000000000000000000000000000
χ4644444-4-44-4-4-244-2-2-2-4-44-2222-2222-2-200002-20000000000000000000000000000000000
χ474444-44-4-44-4-244-2-2-24-4-42-2222-222-2-20000-220000000000000000000000000000000000
χ484444-4-44-4-44-2-4-4-2-2-24-4422-2-22222220000-2-20000000000000000000000000000000000
χ4944-4-444-4-4-444004-4-4000444-4-4-400000000000000000000000000000000000000000000
χ5044-4-444-4-4-44-200-222000-2-2-22220000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000000
χ5144-4-444-4-4-44-200-222000-2-2-22220000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000000
χ5244-4-44-44-44-44004-4-40004-4-44-4400000000000000000000000000000000000000000000
χ5344-4-44-44-44-4-200-222000-222-22-200000000006−66−6−66−6600000000000000000000000000
χ5444-4-44-44-44-4-200-222000-222-22-20000000000−66−666−66−600000000000000000000000000
χ5544-4-4-4444-4-44004-4-4000-44-444-400000000000000000000000000000000000000000000
χ5644-4-4-4444-4-4-200-2220002-22-2-2200000000006−6−666−6−6600000000000000000000000000
χ5744-4-4-4444-4-4-200-2220002-22-2-220000000000−666−6−666−600000000000000000000000000
χ5844-4-4-4-4-44444004-4-4000-4-44-44400000000000000000000000000000000000000000000
χ5944-4-4-4-4-4444-200-22200022-22-2-20000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ6044-4-4-4-4-4444-200-22200022-22-2-20000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ614-4-4400000044-4-4-44000000000004-40000000000000000000000000000002-22-2000000
χ624-4-4400000044-4-4-44000000000004-4000000000000000000000000000000-22-22000000
χ634-4-440000004-44-4-4400000000000-440000000000000000000000000000002-2-22000000
χ644-4-440000004-44-4-4400000000000-44000000000000000000000000000000-222-2000000
χ658-88-8000000800-88-800000000000000000000000000000000000000000000000000000
χ668-88-8000000-4004-4400000000043−43000000000000000000000000000000000000000000
χ678-88-8000000-4004-44000000000−4343000000000000000000000000000000000000000000
χ688-8-88000000-48-844-400000000000-440000000000000000000000000000000000000000
χ698-8-88000000-4-8844-4000000000004-40000000000000000000000000000000000000000

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