Finite Group Databasebeta

← Group #10692759

Character table — Group #10692759

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888881212121216161616161624242424242448484848
order12222234444666121212124444668888121212121212888888121224242424242424242424242424242424888888242424242444884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ6111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ91111-1-11-1-1-1-1111-1-1-1-11-111-1-1ii−i−i1111-1-1i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1ii−i−ii−iii−i−i1-11-1i−i1-1i−i
χ101111-1-11-1-1-1-1111-1-1-1-11-111-1-1ii−i−i1111-1-1i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1−i−iiii−iii−i−i-11-11−ii-11−ii
χ111111-1-11-1-1-1-1111-1-1-1-11-111-1-1ii−i−i1111-1-1i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111ii−i−i−ii−i−iii1-11-1i−i-11−ii
χ121111-1-11-1-1-1-1111-1-1-1-11-111-1-1ii−i−i1111-1-1i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111−i−iii−ii−i−iii-11-11−ii1-1i−i
χ131111-1-11-1-1-1-1111-1-1-1-11-111-1-1−i−iii1111-1-1−ii11-1-11-1−i−i−i−iiiii1111-1-1-1-1ii−i−i−ii−i−iii-11-11i−i-11i−i
χ141111-1-11-1-1-1-1111-1-1-1-11-111-1-1−i−iii1111-1-1−ii11-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−iii−ii−i−iii1-11-1−ii1-1−ii
χ151111-1-11-1-1-1-1111-1-1-1-11-111-1-1−i−iii1111-1-1−ii-1-1111-1−i−i−i−iiiii-1-1-1-11111ii−i−ii−iii−i−i-11-11i−i1-1−ii
χ161111-1-11-1-1-1-1111-1-1-1-11-111-1-1−i−iii1111-1-1−ii-1-1111-1−i−i−i−iiiii-1-1-1-11111−i−iiii−iii−i−i1-11-1−ii-11i−i
χ17222222222-2-22222222-2-2-22220000-2-222-2-2000000-2-20000000000000000000000000022-2-2000000
χ18222222222-2-22222222-2-2-22220000-2-222-2-2000000-2-200000000000000000000000000-2-222000000
χ192222222-2-222222-2-2-2-2-2-22-2222222-2-2-2-222-2-200002-222-2-222-2-20000000000000000000000000000
χ202222222-2-222222-2-2-2-2-2-22-222-2-2-2-2-2-2-2-2222200002-2-2-222-2-2220000000000000000000000000000
χ212222222-2-2-2-2222-2-2-2-222-2-222000022-2-2-2-2000000-2200000000000000002i2i−2i−2i0000000000−2i2i0000
χ222222222-2-2-2-2222-2-2-2-222-2-222000022-2-2-2-2000000-220000000000000000−2i−2i2i2i00000000002i−2i0000
χ23222222-12222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-10000000000
χ24222222-12222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-211110000000000
χ25222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-211110000000000
χ26222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-10000000000
χ27222222-1-2-222-1-1-11111-2-22-2-1-122221111-1-1-2-20000-11-1-111-1-11133−3−333−3−30000003−33−30000000000
χ28222222-1-2-222-1-1-11111-2-22-2-1-122221111-1-1-2-20000-11-1-111-1-111−3−333−3−333000000−33−330000000000
χ29222222-1-2-222-1-1-11111-2-22-2-1-1-2-2-2-21111-1-1220000-1111-1-111-1-133−3−333−3−3000000−33−330000000000
χ30222222-1-2-222-1-1-11111-2-22-2-1-1-2-2-2-21111-1-1220000-1111-1-111-1-1−3−333−3−3330000003−33−30000000000
χ312222-2-22222222222222-2-2-2-2-2000022-2-222000000-2-2000000000000000022220000000000-2-20000
χ322222-2-22222222222222-2-2-2-2-2000022-2-222000000-2-20000000000000000-2-2-2-20000000000220000
χ332222-2-2222-2-22222222-222-2-2-22i2i−2i−2i-2-2-2-2-2-2−2i2i0000222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ342222-2-2222-2-22222222-222-2-2-2−2i−2i2i2i-2-2-2-2-2-22i−2i000022−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ352222-2-22-2-222222-2-2-2-2-22-22-2-20000-2-22222000000-22000000000000000000000000002-2-22000000
χ362222-2-22-2-222222-2-2-2-2-22-22-2-20000-2-22222000000-2200000000000000000000000000-222-2000000
χ372222-2-2-122-2-2-1-1-1-1-1-1-1-222-2112i2i−2i−2i111111−2i2i0000-1-1−i−iiiii−i−i33−3−3−3−333000000i3−i3−i3i30000000000
χ382222-2-2-122-2-2-1-1-1-1-1-1-1-222-2112i2i−2i−2i111111−2i2i0000-1-1−i−iiiii−i−i−3−33333−3−3000000−i3i3i3−i30000000000
χ392222-2-2-122-2-2-1-1-1-1-1-1-1-222-211−2i−2i2i2i1111112i−2i0000-1-1ii−i−i−i−iii33−3−3−3−333000000−i3i3i3−i30000000000
χ402222-2-2-122-2-2-1-1-1-1-1-1-1-222-211−2i−2i2i2i1111112i−2i0000-1-1ii−i−i−i−iii−3−33333−3−3000000i3−i3−i3i30000000000
χ412222-2-2-1-2-2-2-2-1-1-111112-222112i2i−2i−2i-1-1-1-1112i−2i22-2-2-11−i−i−i−iiiii-1-1-1-1111100002i−2i−i−iii0000000000
χ422222-2-2-1-2-2-2-2-1-1-111112-222112i2i−2i−2i-1-1-1-1112i−2i-2-222-11−i−i−i−iiiii1111-1-1-1-10000−2i2iii−i−i0000000000
χ432222-2-2-1-2-2-2-2-1-1-111112-22211−2i−2i2i2i-1-1-1-111−2i2i22-2-2-11iiii−i−i−i−i-1-1-1-111110000−2i2iii−i−i0000000000
χ442222-2-2-1-2-2-2-2-1-1-111112-22211−2i−2i2i2i-1-1-1-111−2i2i-2-222-11iiii−i−i−i−i1111-1-1-1-100002i−2i−i−iii0000000000
χ45444444-244-4-4-2-2-2-2-2-2-2-4-4-44-2-2000022-2-22200000022000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2222244-4-4-2-20000-2-222220000002-2000000000000000000000000000000000000
χ474444-4-4-24444-2-2-2-2-2-2-24-4-4-4220000-2-222-2-200000022000000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-22222-44-4422000022-2-2-2-20000002-2000000000000000000000000000000000000
χ4944-4-44-4400004-4-4000000004-422−2222−220000000000000022−220022−22000000000000000000000000000000
χ5044-4-44-4400004-4-4000000004-4−2222−222200000000000000−222200−2222000000000000000000000000000000
χ5144-4-44-4-20000-2222323−23−230000-2222−2222−220023−230000000000−226−6−226−60000000000000000000000000000
χ5244-4-44-4-20000-2222323−23−230000-22−2222−22220023−2300000000002−2−662−2−660000000000000000000000000000
χ5344-4-44-4-20000-222−23−2323230000-2222−2222−2200−23230000000000−22−66−22−660000000000000000000000000000
χ5444-4-44-4-20000-222−23−2323230000-22−2222−222200−232300000000002−26−62−26−60000000000000000000000000000
χ5544-4-4-44400004-4-400000000-44−2i22i22i2−2i200000000000000−2i22i2002i2−2i2000000000000000000000000000000
χ5644-4-4-44400004-4-400000000-442i2−2i2−2i22i2000000000000002i2−2i200−2i22i2000000000000000000000000000000
χ5744-4-4-44-20000-2222323−23−2300002-2−2i22i22i2−2i200−23230000000000i2−i2i6−i6−i2i2−i6i60000000000000000000000000000
χ5844-4-4-44-20000-2222323−23−2300002-22i2−2i2−2i22i200−23230000000000−i2i2−i6i6i2−i2i6−i60000000000000000000000000000
χ5944-4-4-44-20000-222−23−23232300002-2−2i22i22i2−2i20023−230000000000i2−i2−i6i6−i2i2i6−i60000000000000000000000000000
χ6044-4-4-44-20000-222−23−23232300002-22i2−2i2−2i22i20023−230000000000−i2i2i6−i6i2−i2−i6i60000000000000000000000000000
χ614-44-4004004i−4i-44-40000000000000000004i−4i002-22i−2i00000000002-22-22i−2i2i−2i00000000000000000000
χ624-44-4004004i−4i-44-40000000000000000004i−4i00-22−2i2i0000000000-22-22−2i2i−2i2i00000000000000000000
χ634-44-400400−4i4i-44-4000000000000000000−4i4i002-2−2i2i00000000002-22-2−2i2i−2i2i00000000000000000000
χ644-44-400400−4i4i-44-4000000000000000000−4i4i00-222i−2i0000000000-22-222i−2i2i−2i00000000000000000000
χ654-44-400-2004i−4i2-22−2i32i3−2i32i3000000000023−2300−2i2i002-22i−2i0000000000−1+31−3−1−31+3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000
χ664-44-400-2004i−4i2-22−2i32i3−2i32i3000000000023−2300−2i2i00-22−2i2i00000000001−3−1+31+3−1−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000
χ674-44-400-2004i−4i2-222i3−2i32i3−2i30000000000−232300−2i2i002-22i−2i0000000000−1−31+3−1+31−3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000
χ684-44-400-2004i−4i2-222i3−2i32i3−2i30000000000−232300−2i2i00-22−2i2i00000000001+3−1−31−3−1+3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000000000
χ694-44-400-200−4i4i2-22−2i32i3−2i32i30000000000−2323002i−2i002-2−2i2i0000000000−1−31+3−1+31−3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000000000
χ704-44-400-200−4i4i2-22−2i32i3−2i32i30000000000−2323002i−2i00-222i−2i00000000001+3−1−31−3−1+3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000
χ714-44-400-200−4i4i2-222i3−2i32i3−2i3000000000023−23002i−2i002-2−2i2i0000000000−1+31−3−1−31+3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000
χ724-44-400-200−4i4i2-222i3−2i32i3−2i3000000000023−23002i−2i00-222i−2i00000000001−3−1+31+3−1−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000
χ734-4-440044i−4i00-4-444i−4i−4i4i00000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000
χ744-4-440044i−4i00-4-444i−4i−4i4i0000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000
χ754-4-44004−4i4i00-4-44−4i4i4i−4i00000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000
χ764-4-44004−4i4i00-4-44−4i4i4i−4i0000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000
χ778-8-8800-48i−8i0044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ788-8-8800-4−8i8i0044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000

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