Finite Group Databasebeta

← Group #10693210

Character table — Group #10693210

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888888888888888161616161616242424242424242448484848
order122222344666666622444666688881212121222226666666688121224242424242424244412121212244488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ91111-1-11-1-111-1-11-1-11-111-111-1-1ii−i−i11-1-111-1-11111-1-1-1-1i−i1-1iiii−i−i−i−ii−iii−i−i11-1-1ii−i−i1-1i−i
χ101111-1-11-1-111-1-11-1-11-111-111-1-1ii−i−i11-1-111-1-11111-1-1-1-1i−i1-1iiii−i−i−i−ii−iii−i−i-1-111−i−iii-11−ii
χ111111-1-11-1-111-1-11-1-11-111-111-1-1ii−i−i11-1-1-1-111-1-1-1-11111i−i1-1iiii−i−i−i−i−ii−i−iii11-1-1ii−i−i-11−ii
χ121111-1-11-1-111-1-11-1-11-111-111-1-1ii−i−i11-1-1-1-111-1-1-1-11111i−i1-1iiii−i−i−i−i−ii−i−iii-1-111−i−iii1-1i−i
χ131111-1-11-1-111-1-11-1-11-111-111-1-1−i−iii11-1-111-1-11111-1-1-1-1−ii1-1−i−i−i−iiiii−ii−i−iii11-1-1−i−iii1-1−ii
χ141111-1-11-1-111-1-11-1-11-111-111-1-1−i−iii11-1-111-1-11111-1-1-1-1−ii1-1−i−i−i−iiiii−ii−i−iii-1-111ii−i−i-11i−i
χ151111-1-11-1-111-1-11-1-11-111-111-1-1−i−iii11-1-1-1-111-1-1-1-11111−ii1-1−i−i−i−iiiiii−iii−i−i11-1-1−i−iii-11i−i
χ161111-1-11-1-111-1-11-1-11-111-111-1-1−i−iii11-1-1-1-111-1-1-1-11111−ii1-1−i−i−i−iiiiii−iii−i−i-1-111ii−i−i1-1−ii
χ172222222222222222-2-22-2-2-2-2-2-222222222000000000000-2-2-2-222-2-222-2-2000000000000000000
χ182222222222222222-2-22-2-2-2-2-2-2-2-2-2-2222200000000000022-2-2-2-222-2-222000000000000000000
χ192222222-2-2222222222-2-2-222220000-2-2-2-200000000000000-2-20000000000000000002i−2i2i−2i0000
χ202222222-2-2222222222-2-2-222220000-2-2-2-200000000000000-2-2000000000000000000−2i2i−2i2i0000
χ212222222-2-22222222-2-2-222-2-2-2-20000-2-2-2-20000000000000022000000000000002-22-200000000
χ222222222-2-22222222-2-2-222-2-2-2-20000-2-2-2-2000000000000002200000000000000-22-2200000000
χ23222222-122-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ24222222-122-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-2-2-2-21111111122-1-1-1-1-1-1-1-1-1-1-2-21111000000000000
χ25222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-1-111111111-2-21111000000000000
χ26222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-2-1-1-1-1-2-2-2-211111111-2-2-1-11111111122-1-1-1-1000000000000
χ27222222-122-1-1-1-1-1-1-1-2-22-2-211112222-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-2-211-1-111-1-11100−i3i3−i3i3000000000000
χ28222222-122-1-1-1-1-1-1-1-2-22-2-211112222-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-2-211-1-111-1-11100i3−i3i3−i3000000000000
χ29222222-122-1-1-1-1-1-1-1-2-22-2-21111-2-2-2-2-1-1-1-10000−i3−i3i3i3−i3−i3i3i3221111-1-111-1-100i3−i3i3−i3000000000000
χ30222222-122-1-1-1-1-1-1-1-2-22-2-21111-2-2-2-2-1-1-1-10000i3i3−i3−i3i3i3−i3−i3221111-1-111-1-100−i3i3−i3i3000000000000
χ312222-2-222222-2-22-2-22-2-2-2222-2-20000-2-22200000000000000-220000000000000000002-2-220000
χ322222-2-222222-2-22-2-22-2-2-2222-2-20000-2-22200000000000000-22000000000000000000-222-20000
χ332222-2-222222-2-22-2-2-22-22-2-2-2220000-2-222000000000000002-2000000000000002-2-2200000000
χ342222-2-222222-2-22-2-2-22-22-2-2-2220000-2-222000000000000002-200000000000000-222-200000000
χ352222-2-22-2-222-2-22-2-2-222-22-2-2222i2i−2i−2i22-2-2000000000000−2i2i-222i2i−2i−2i−2i−2i2i2i000000000000000000
χ362222-2-22-2-222-2-22-2-2-222-22-2-222−2i−2i2i2i22-2-20000000000002i−2i-22−2i−2i2i2i2i2i−2i−2i000000000000000000
χ372222-2-2-1-2-2-1-111-1112-222-2-1-1112i2i−2i−2i-1-11122-2-2-1-1-1-111112i−2i-11−i−i−i−iiiii2i−2i−i−iii000000000000
χ382222-2-2-1-2-2-1-111-1112-222-2-1-1112i2i−2i−2i-1-111-2-2221111-1-1-1-12i−2i-11−i−i−i−iiiii−2i2iii−i−i000000000000
χ392222-2-2-1-2-2-1-111-1112-222-2-1-111−2i−2i2i2i-1-11122-2-2-1-1-1-11111−2i2i-11iiii−i−i−i−i−2i2iii−i−i000000000000
χ402222-2-2-1-2-2-1-111-1112-222-2-1-111−2i−2i2i2i-1-111-2-2221111-1-1-1-1−2i2i-11iiii−i−i−i−i2i−2i−i−iii000000000000
χ412222-2-2-1-2-2-1-111-111-222-2211-1-12i2i−2i−2i-1-1110000−i3−i3i3i3i3i3−i3−i3−2i2i1-1−i−iiiii−i−i003−3−33000000000000
χ422222-2-2-1-2-2-1-111-111-222-2211-1-12i2i−2i−2i-1-1110000i3i3−i3−i3−i3−i3i3i3−2i2i1-1−i−iiiii−i−i00−333−3000000000000
χ432222-2-2-1-2-2-1-111-111-222-2211-1-1−2i−2i2i2i-1-1110000−i3−i3i3i3i3i3−i3−i32i−2i1-1ii−i−i−i−iii00−333−3000000000000
χ442222-2-2-1-2-2-1-111-111-222-2211-1-1−2i−2i2i2i-1-1110000i3i3−i3−i3−i3−i3i3i32i−2i1-1ii−i−i−i−iii003−3−33000000000000
χ45444444-2-4-4-2-2-2-2-2-2-244-4-4-4-2-2-2-200002222000000000000002200000000000000000000000000
χ46444444-2-4-4-2-2-2-2-2-2-2-4-4-44422220000222200000000000000-2-200000000000000000000000000
χ474444-4-4-244-2-222-2224-4-4-44-2-222000022-2-2000000000000002-200000000000000000000000000
χ484444-4-4-244-2-222-222-44-44-422-2-2000022-2-200000000000000-2200000000000000000000000000
χ4944-4-44-44004-444-4-4-4000000000−2i22i2−2i22i200000000000000000000−2i22i200−2i22i200000000000000000000
χ5044-4-44-44004-444-4-4-40000000002i2−2i22i2−2i2000000000000000000002i2−2i2002i2−2i200000000000000000000
χ5144-4-44-4-200-22-2-222200000−2i32i3−2i32i3−2i22i2−2i22i200000000000000000000i2−i26−6i2−i26−6000000000000000000
χ5244-4-44-4-200-22-2-222200000−2i32i3−2i32i32i2−2i22i2−2i200000000000000000000−i2i2−66−i2i2−66000000000000000000
χ5344-4-44-4-200-22-2-2222000002i3−2i32i3−2i3−2i22i2−2i22i200000000000000000000i2−i2−66i2−i2−66000000000000000000
χ5444-4-44-4-200-22-2-2222000002i3−2i32i3−2i32i2−2i22i2−2i200000000000000000000−i2i26−6−i2i26−6000000000000000000
χ5544-4-4-444004-4-4-4-44400000000022−22−22220000000000000000000022−2200−222200000000000000000000
χ5644-4-4-444004-4-4-4-444000000000−222222−2200000000000000000000−22220022−2200000000000000000000
χ5744-4-4-44-200-22222-2-200000−2i32i32i3−2i322−22−222200000000000000000000−22i6−i62−2−i6i6000000000000000000
χ5844-4-4-44-200-22222-2-200000−2i32i32i3−2i3−222222−22000000000000000000002−2−i6i6−22i6−i6000000000000000000
χ5944-4-4-44-200-22222-2-2000002i3−2i3−2i32i322−22−222200000000000000000000−22−i6i62−2i6−i6000000000000000000
χ6044-4-4-44-200-22222-2-2000002i3−2i3−2i32i3−222222−22000000000000000000002−2i6−i6−22−i6i6000000000000000000
χ614-4-440044-4-4-4004000000000000000004-42-22-22-22-22-22-2000000000000000000000000000000
χ624-4-440044-4-4-4004000000000000000004-4-22-22-22-22-22-22000000000000000000000000000000
χ634-4-44004-44-4-400400000000000000000-442-2-222-22-2-22-22000000000000000000000000000000
χ644-4-44004-44-4-400400000000000000000-44-222-2-22-222-22-2000000000000000000000000000000
χ654-4-4400-24-422−2i32i3-2−2i32i30000000000000−2i32i3-222-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000000
χ664-4-4400-24-422−2i32i3-2−2i32i30000000000000−2i32i3-22-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000000
χ674-4-4400-24-4222i3−2i3-22i3−2i300000000000002i3−2i3-222-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000000
χ684-4-4400-24-4222i3−2i3-22i3−2i300000000000002i3−2i3-22-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000000
χ694-4-4400-2-4422−2i32i3-2−2i32i300000000000002i3−2i32-22-2-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3000000000000000000000000000000
χ704-4-4400-2-4422−2i32i3-2−2i32i300000000000002i3−2i32-2-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000
χ714-4-4400-2-44222i3−2i3-22i3−2i30000000000000−2i32i32-22-2-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3000000000000000000000000000000
χ724-4-4400-2-44222i3−2i3-22i3−2i30000000000000−2i32i32-2-222-21+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000
χ738-88-800800-8800-80000000000000000000000000000000000000000000000000000000000000
χ748-88-800-4004-4−4i34i344i3−4i300000000000000000000000000000000000000000000000000000000000
χ758-88-800-4004-44i3−4i34−4i34i300000000000000000000000000000000000000000000000000000000000

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