Finite Group Databasebeta

← Group #10692968

Character table — Group #10692968

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order122222222234466666664446666121212122222666666668888121224242424242424244412121212244488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ911111-1-1-11-11-1-111-1-11-1-111-111-1-111-1-111-1-11111-1-1-1-1ii−i−i1-1iiii−i−i−i−ii−iii−i−i11-1-1ii−i−i1-1i−i
χ1011111-1-1-11-11-1-111-1-11-1-111-111-1-111-1-111-1-11111-1-1-1-1ii−i−i1-1iiii−i−i−i−ii−iii−i−i-1-111−i−iii-11−ii
χ1111111-1-1-11-11-1-111-1-11-1-111-111-1-111-1-111-1-11111-1-1-1-1−i−iii1-1−i−i−i−iiiii−ii−i−iii11-1-1−i−iii1-1−ii
χ1211111-1-1-11-11-1-111-1-11-1-111-111-1-111-1-111-1-11111-1-1-1-1−i−iii1-1−i−i−i−iiiii−ii−i−iii-1-111ii−i−i-11i−i
χ1311111-1-1-11-11-1-111-1-11-1-111-111-1-111-1-1-1-111-1-1-1-11111ii−i−i1-1iiii−i−i−i−i−ii−i−iii11-1-1ii−i−i-11−ii
χ1411111-1-1-11-11-1-111-1-11-1-111-111-1-111-1-1-1-111-1-1-1-11111ii−i−i1-1iiii−i−i−i−i−ii−i−iii-1-111−i−iii1-1i−i
χ1511111-1-1-11-11-1-111-1-11-1-111-111-1-111-1-1-1-111-1-1-1-11111−i−iii1-1−i−i−i−iiiiii−iii−i−i11-1-1−i−iii-11i−i
χ1611111-1-1-11-11-1-111-1-11-1-111-111-1-111-1-1-1-111-1-1-1-11111−i−iii1-1−i−i−i−iiiiii−iii−i−i-1-111ii−i−i1-1−ii
χ1722222222222-2-22222222-2-2-22222-2-2-2-20000000000000000-2-2000000000000002-22-200000000
χ1822222222222-2-22222222-2-2-22222-2-2-2-20000000000000000-2-200000000000000-22-2200000000
χ192222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ202222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-21111000000000000
χ212222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-1-1-2-21111000000000000
χ222222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2-1-11111111122-1-1-1-1000000000000
χ2322222-2-2-22-222222-2-22-2-2-2-2222-2-2-2-2220000000000000000-22000000000000002-2-2200000000
χ2422222-2-2-22-222222-2-22-2-2-2-2222-2-2-2-2220000000000000000-2200000000000000-222-200000000
χ2522222-2-2-22-2-1-2-2-1-111-11122-2-1-111-1-11122-2-2-1-1-1-111112i2i−2i−2i-11−i−i−i−iiiii2i−2i−i−iii000000000000
χ2622222-2-2-22-2-1-2-2-1-111-11122-2-1-111-1-11122-2-2-1-1-1-11111−2i−2i2i2i-11iiii−i−i−i−i−2i2iii−i−i000000000000
χ2722222-2-2-22-2-1-2-2-1-111-11122-2-1-111-1-111-2-2221111-1-1-1-12i2i−2i−2i-11−i−i−i−iiiii−2i2iii−i−i000000000000
χ2822222-2-2-22-2-1-2-2-1-111-11122-2-1-111-1-111-2-2221111-1-1-1-1−2i−2i2i2i-11iiii−i−i−i−i2i−2i−i−iii000000000000
χ292222-22-22-2-222222222222-2-2-2-2-2-222220000000000002-22-2-2-222-2-222-2-2000000000000000000
χ302222-22-22-2-222222222222-2-2-2-2-2-22222000000000000-22-22-2-2-2-222-2-222000000000000000000
χ312222-22-22-2-22-2-22222222-222-2-2-2-2-2-2-2-20000000000000000220000000000000000002i−2i2i−2i0000
χ322222-22-22-2-22-2-22222222-222-2-2-2-2-2-2-2-2000000000000000022000000000000000000−2i2i−2i2i0000
χ332222-22-22-2-2-122-1-1-1-1-1-1-12-2-21111-1-1-1-10000−i3−i3i3i3−i3−i3i3i32-22-211-1-111-1-11100−i3i3−i3i3000000000000
χ342222-22-22-2-2-122-1-1-1-1-1-1-12-2-21111-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-22-221111-1-111-1-100i3−i3i3−i3000000000000
χ352222-22-22-2-2-122-1-1-1-1-1-1-12-2-21111-1-1-1-10000i3i3−i3−i3i3i3−i3−i32-22-211-1-111-1-11100i3−i3i3−i3000000000000
χ362222-22-22-2-2-122-1-1-1-1-1-1-12-2-21111-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-22-221111-1-111-1-100−i3i3−i3i3000000000000
χ372222-2-22-2-2222222-2-22-2-2-22-2-2-222-2-22200000000000000002-20000000000000000002-2-220000
χ382222-2-22-2-2222222-2-22-2-2-22-2-2-222-2-22200000000000000002-2000000000000000000-222-20000
χ392222-2-22-2-222-2-222-2-22-2-22-22-2-22222-2-20000000000002i−2i−2i2i-222i2i−2i−2i−2i−2i2i2i000000000000000000
χ402222-2-22-2-222-2-222-2-22-2-22-22-2-22222-2-2000000000000−2i2i2i−2i-22−2i−2i2i2i2i2i−2i−2i000000000000000000
χ412222-2-22-2-22-1-2-2-1-111-1112-2211-1-1-1-1110000−i3−i3i3i3i3i3−i3−i32i−2i−2i2i1-1−i−iiiii−i−i003−3−33000000000000
χ422222-2-22-2-22-1-2-2-1-111-1112-2211-1-1-1-1110000−i3−i3i3i3i3i3−i3−i3−2i2i2i−2i1-1ii−i−i−i−iii00−333−3000000000000
χ432222-2-22-2-22-1-2-2-1-111-1112-2211-1-1-1-1110000i3i3−i3−i3−i3−i3i3i32i−2i−2i2i1-1−i−iiiii−i−i00−333−3000000000000
χ442222-2-22-2-22-1-2-2-1-111-1112-2211-1-1-1-1110000i3i3−i3−i3−i3−i3i3i3−2i2i2i−2i1-1ii−i−i−i−iii003−3−33000000000000
χ454444444444-2-4-4-2-2-2-2-2-2-2-4-4-4-2-2-2-2222200000000000000002200000000000000000000000000
χ4644444-4-4-44-4-244-2-222-222-4-44-2-22222-2-200000000000000002-200000000000000000000000000
χ474444-44-44-4-4-2-4-4-2-2-2-2-2-2-2-444222222220000000000000000-2-200000000000000000000000000
χ484444-4-44-4-44-244-2-222-222-44-422-2-222-2-20000000000000000-2200000000000000000000000000
χ4944-4-4444-4-4-44004-444-4-4-40004-44-4000000000000000000000000000000000000000000000000
χ5044-4-4444-4-4-4-200-22-2-2222000-22-2200000000000000000000006−66−66−66−6000000000000000000
χ5144-4-4444-4-4-4-200-22-2-2222000-22-220000000000000000000000−66−66−66−66000000000000000000
χ5244-4-44-4-44-444004-4-4-4-4440004-4-44000000000000000000000000000000000000000000000000
χ5344-4-44-4-44-44-200-22222-2-2000-222-20000000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000
χ5444-4-44-4-44-44-200-22222-2-2000-222-20000000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000
χ5544-4-4-44-4-4444004-444-4-4-4000-44-44000000000000000000000000000000000000000000000000
χ5644-4-4-44-4-444-200-22-2-22220002-22-200000000000000000000006−6−666−6−66000000000000000000
χ5744-4-4-44-4-444-200-22-2-22220002-22-20000000000000000000000−666−6−666−6000000000000000000
χ5844-4-4-4-4444-44004-4-4-4-444000-444-4000000000000000000000000000000000000000000000000
χ5944-4-4-4-4444-4-200-22222-2-20002-2-220000000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000
χ6044-4-4-4-4444-4-200-22222-2-20002-2-220000000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000
χ614-4-4400000044-4-4-4004000000000004-42-22-22-22-22-22-200000000000000000000000000000000
χ624-4-4400000044-4-4-4004000000000004-4-22-22-22-22-22-2200000000000000000000000000000000
χ634-4-440000004-44-4-400400000000000-442-2-222-22-2-22-2200000000000000000000000000000000
χ644-4-440000004-44-4-400400000000000-44-222-2-22-222-22-200000000000000000000000000000000
χ654-4-44000000-24-422−2i32i3-2−2i32i30000000−2i32i3-222-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000000000000000
χ664-4-44000000-24-422−2i32i3-2−2i32i30000000−2i32i3-22-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000000000000000
χ674-4-44000000-24-4222i3−2i3-22i3−2i300000002i3−2i3-222-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000000000000000
χ684-4-44000000-24-4222i3−2i3-22i3−2i300000002i3−2i3-22-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000000000000000
χ694-4-44000000-2-4422−2i32i3-2−2i32i300000002i3−2i32-22-2-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000000000
χ704-4-44000000-2-4422−2i32i3-2−2i32i300000002i3−2i32-2-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000000000000000
χ714-4-44000000-2-44222i3−2i3-22i3−2i30000000−2i32i32-22-2-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000000000000000
χ724-4-44000000-2-44222i3−2i3-22i3−2i30000000−2i32i32-2-222-21+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000000000000000
χ738-88-8000000800-8800-8000000000000000000000000000000000000000000000000000000000
χ748-88-8000000-4004-4−4i34i344i3−4i30000000000000000000000000000000000000000000000000000000
χ758-88-8000000-4004-44i3−4i34−4i34i30000000000000000000000000000000000000000000000000000000

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