Finite Group Databasebeta

← Group #10692463

Character table — Group #10692463

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888888888888888161616161616242424242424242448484848
order122222344666666644444888812121212121212124444881212121212121212121224242424242424244412121212244488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ91111-1-11-1-1-1-111-1-111-111-1ii−i−i11-1-111-1-1ii−i−ii−i1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-111-1-1i−ii−ii−i1-1
χ101111-1-11-1-1-1-111-1-111-111-1ii−i−i11-1-111-1-1ii−i−ii−i1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1-1-111−ii−ii−ii-11
χ111111-1-11-1-1-1-111-1-111-111-1ii−i−i11-1-111-1-1−i−iiii−i1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-11111-1-1i−ii−i−ii-11
χ121111-1-11-1-1-1-111-1-111-111-1ii−i−i11-1-111-1-1−i−iiii−i1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-1-111−ii−iii−i1-1
χ131111-1-11-1-1-1-111-1-111-111-1−i−iii11-1-111-1-1ii−i−i−ii1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-11111-1-1−ii−iii−i-11
χ141111-1-11-1-1-1-111-1-111-111-1−i−iii11-1-111-1-1ii−i−i−ii1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111-1-111i−ii−i−ii1-1
χ151111-1-11-1-1-1-111-1-111-111-1−i−iii11-1-111-1-1−i−iii−ii1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-111-1-1−ii−ii−ii1-1
χ161111-1-11-1-1-1-111-1-111-111-1−i−iii11-1-111-1-1−i−iii−ii1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1-1-111i−ii−ii−i-11
χ172222222222222222-2-22-2-22222-2-2-2-222220000-2-2-2-20000000022-2-222-2-2000000000000000000
χ182222222222222222-2-22-2-2-2-2-2-2-2-2-2-22222000022-2-200000000-2-222-2-222000000000000000000
χ192222222-2-2222222222-2-2-200002222-2-2-2-2000000-2-2000000000000000000000000002i−2i−2i2i0000
χ202222222-2-2222222222-2-2-200002222-2-2-2-2000000-2-200000000000000000000000000−2i2i2i−2i0000
χ212222222-2-22222222-2-2-2220000-2-2-2-2-2-2-2-20000002200000000000000000000002-22-200000000
χ222222222-2-22222222-2-2-2220000-2-2-2-2-2-2-2-2000000220000000000000000000000-22-2200000000
χ23222222-122-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ24222222-122-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ25222222-122-1-1-1-1-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ26222222-122-1-1-1-1-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ27222222-122-1-1-1-1-1-1-1-2-22-2-222221111-1-1-1-10000-2-211−i3−i3i3i3−i3−i3i3i3-1-111-1-11100−i3i3−i3i3000000000000
χ28222222-122-1-1-1-1-1-1-1-2-22-2-222221111-1-1-1-10000-2-211i3i3−i3−i3i3i3−i3−i3-1-111-1-11100i3−i3i3−i3000000000000
χ29222222-122-1-1-1-1-1-1-1-2-22-2-2-2-2-2-21111-1-1-1-100002211−i3−i3i3i3−i3−i3i3i311-1-111-1-100i3−i3i3−i3000000000000
χ30222222-122-1-1-1-1-1-1-1-2-22-2-2-2-2-2-21111-1-1-1-100002211i3i3−i3−i3i3i3−i3−i311-1-111-1-100−i3i3−i3i3000000000000
χ312222-2-2222-2-222-2-222-2-2-22000022-2-2-2-222000000-220000000000000000000000000022-2-20000
χ322222-2-2222-2-222-2-222-2-2-22000022-2-2-2-222000000-2200000000000000000000000000-2-2220000
χ332222-2-2222-2-222-2-22-22-22-20000-2-222-2-2220000002-200000000000000000000002-2-2200000000
χ342222-2-2222-2-222-2-22-22-22-20000-2-222-2-2220000002-20000000000000000000000-222-200000000
χ352222-2-22-2-2-2-222-2-22-222-222i2i−2i−2i-2-22222-2-20000−2i2i-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ362222-2-22-2-2-2-222-2-22-222-22−2i−2i2i2i-2-22222-2-200002i−2i-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ372222-2-2-1-2-211-1-111-12-222-22i2i−2i−2i-1-111-1-1112i2i−2i−2i2i−2i-11−i−i−i−iiiii−i−i−i−iiiii2-2-1-111000000000000
χ382222-2-2-1-2-211-1-111-12-222-22i2i−2i−2i-1-111-1-111−2i−2i2i2i2i−2i-11iiii−i−i−i−i−i−i−i−iiiii-2211-1-1000000000000
χ392222-2-2-1-2-211-1-111-12-222-2−2i−2i2i2i-1-111-1-1112i2i−2i−2i−2i2i-11−i−i−i−iiiiiiiii−i−i−i−i-2211-1-1000000000000
χ402222-2-2-1-2-211-1-111-12-222-2−2i−2i2i2i-1-111-1-111−2i−2i2i2i−2i2i-11iiii−i−i−i−iiiii−i−i−i−i2-2-1-111000000000000
χ412222-2-2-1-2-211-1-111-1-222-222i2i−2i−2i11-1-1-1-1110000−2i2i1-133−3−3−3−333−i−iiiii−i−i00−i3i3i3−i3000000000000
χ422222-2-2-1-2-211-1-111-1-222-222i2i−2i−2i11-1-1-1-1110000−2i2i1-1−3−33333−3−3−i−iiiii−i−i00i3−i3−i3i3000000000000
χ432222-2-2-1-2-211-1-111-1-222-22−2i−2i2i2i11-1-1-1-11100002i−2i1-133−3−3−3−333ii−i−i−i−iii00i3−i3−i3i3000000000000
χ442222-2-2-1-2-211-1-111-1-222-22−2i−2i2i2i11-1-1-1-11100002i−2i1-1−3−33333−3−3ii−i−i−i−iii00−i3i3i3−i3000000000000
χ45444444-2-4-4-2-2-2-2-2-2-244-4-4-40000-2-2-2-22222000000220000000000000000000000000000000000
χ46444444-2-4-4-2-2-2-2-2-2-2-4-4-444000022222222000000-2-20000000000000000000000000000000000
χ474444-4-4-24422-2-222-24-4-4-440000-2-22222-2-20000002-20000000000000000000000000000000000
χ484444-4-4-24422-2-222-2-44-44-4000022-2-222-2-2000000-220000000000000000000000000000000000
χ4944-4-44-4400444-4-4-4-40000022−2222−2200000000000000000000000022−220022−2200000000000000000000
χ5044-4-44-4400444-4-4-4-400000−2222−2222000000000000000000000000−222200−222200000000000000000000
χ5144-4-44-4-200-2-2-222220000022−2222−22−2i32i3−2i32i300000000000000000000−22i6−i6−22i6−i6000000000000000000
χ5244-4-44-4-200-2-2-222220000022−2222−222i3−2i32i3−2i300000000000000000000−22−i6i6−22−i6i6000000000000000000
χ5344-4-44-4-200-2-2-2222200000−2222−2222−2i32i3−2i32i3000000000000000000002−2−i6i62−2−i6i6000000000000000000
χ5444-4-44-4-200-2-2-2222200000−2222−22222i3−2i32i3−2i3000000000000000000002−2i6−i62−2i6−i6000000000000000000
χ5544-4-4-44400-4-44-444-400000−2i22i22i2−2i2000000000000000000000000−2i22i2002i2−2i200000000000000000000
χ5644-4-4-44400-4-44-444-4000002i2−2i2−2i22i20000000000000000000000002i2−2i200−2i22i200000000000000000000
χ5744-4-4-44-20022-22-2-2200000−2i22i22i2−2i2−2i32i32i3−2i300000000000000000000i2−i26−6−i2i2−66000000000000000000
χ5844-4-4-44-20022-22-2-2200000−2i22i22i2−2i22i3−2i3−2i32i300000000000000000000i2−i2−66−i2i26−6000000000000000000
χ5944-4-4-44-20022-22-2-22000002i2−2i2−2i22i2−2i32i32i3−2i300000000000000000000−i2i2−66i2−i26−6000000000000000000
χ6044-4-4-44-20022-22-2-22000002i2−2i2−2i22i22i3−2i3−2i32i300000000000000000000−i2i26−6i2−i2−66000000000000000000
χ614-4-440044-400-4-40040000000000000004-42i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ624-4-440044-400-4-40040000000000000004-4−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ634-4-44004-4400-4-4004000000000000000-442-2-2200002-22-2-22-2200000000000000000000000000
χ644-4-44004-4400-4-4004000000000000000-44-222-20000-22-222-22-200000000000000000000000000
χ654-4-4400-24-4−2i32i322−2i32i3-20000000000000−2i32i3-222i−2i2i−2i00002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ2200000000000000000000000000
χ664-4-4400-24-4−2i32i322−2i32i3-20000000000000−2i32i3-22−2i2i−2i2i0000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ2200000000000000000000000000
χ674-4-4400-24-42i3−2i3222i3−2i3-200000000000002i3−2i3-222i−2i2i−2i00002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ1400000000000000000000000000
χ684-4-4400-24-42i3−2i3222i3−2i3-200000000000002i3−2i3-22−2i2i−2i2i0000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ1400000000000000000000000000
χ694-4-4400-2-44−2i32i322−2i32i3-200000000000002i3−2i32-22-2-220000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ704-4-4400-2-44−2i32i322−2i32i3-200000000000002i3−2i32-2-222-200001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ714-4-4400-2-442i3−2i3222i3−2i3-20000000000000−2i32i32-22-2-220000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ724-4-4400-2-442i3−2i3222i3−2i3-20000000000000−2i32i32-2-222-200001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ738-88-80080000-8800-800000000000000000000000000000000000000000000000000000000000
χ748-88-800-400−4i34i34-44i3−4i3400000000000000000000000000000000000000000000000000000000000
χ758-88-800-4004i3−4i34-4−4i34i3400000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.