Finite Group Databasebeta

← Group #10691007

Character table — Group #10691007

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order122222344444466644466121212121212121288888888121224242424242424242244888824661212242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1
χ91111-1-11-1-111-1-111111-1-1-111-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−i11-1-1ii−i−i1-111-1-1ii−i−i-11ii−i−ii−i1-1
χ101111-1-11-1-111-1-111111-1-1-111-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−i-1-111−i−iii1-111-1-1ii−i−i1-1−i−iii−ii-11
χ111111-1-11-1-111-1-111111-1-1-111-1-1-1-1-1-1ii−i−i−i−iii11−i−i−i−iiiii11-1-1ii−i−i-11-1-111ii−i−i-11−i−iiii−i-11
χ121111-1-11-1-111-1-111111-1-1-111-1-1-1-1-1-1ii−i−i−i−iii11−i−i−i−iiiii-1-111−i−iii-11-1-111ii−i−i1-1ii−i−i−ii1-1
χ131111-1-11-1-111-1-111111-1-1-111-1-1-1-1-1-1−i−iiiii−i−i11iiii−i−i−i−i11-1-1−i−iii-11-1-111−i−iii-11ii−i−i−ii-11
χ141111-1-11-1-111-1-111111-1-1-111-1-1-1-1-1-1−i−iiiii−i−i11iiii−i−i−i−i-1-111ii−i−i-11-1-111−i−iii1-1−i−iiii−i1-1
χ151111-1-11-1-111-1-111111-1-1-111-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii11-1-1−i−iii1-111-1-1−i−iii-11−i−iii−ii1-1
χ161111-1-11-1-111-1-111111-1-1-111-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii-1-111ii−i−i1-111-1-1−i−iii1-1ii−i−ii−i-11
χ17222222222-2-2-2-22222-2-222-2-222-2-2-2-22i−2i2i−2i0000-2200000000000000000000002i−2i2i−2i0000000000
χ18222222222-2-2-2-22222-2-222-2-222-2-2-2-2−2i2i−2i2i0000-220000000000000000000000−2i2i−2i2i0000000000
χ192222222-2-222-2-2222-2-222222-2-222-2-200000000-2-20000000022-2-2000000000000002-200000000
χ202222222-2-222-2-2222-2-222222-2-222-2-200000000-2-200000000-2-22200000000000000-2200000000
χ212222222-2-2-2-222222-22-222-2-2-2-2-2-222000000002-200000000000022220000000000000000-2-200
χ222222222-2-2-2-222222-22-222-2-2-2-2-2-222000000002-2000000000000-2-2-2-200000000000000002200
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-21111-1-1-1-10000000000
χ25222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ26222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000000022-1-1-1-111110000000000
χ27222222-122-2-2-2-2-1-1-12-2-2-1-111-1-111112i−2i2i−2i00001-133−3−333−3−30000000000−i3i3−i3i3−ii−ii0000000000
χ28222222-122-2-2-2-2-1-1-12-2-2-1-111-1-111112i−2i2i−2i00001-1−3−333−3−3330000000000i3−i3i3−i3−ii−ii0000000000
χ29222222-122-2-2-2-2-1-1-12-2-2-1-111-1-11111−2i2i−2i2i00001-133−3−333−3−30000000000i3−i3i3−i3i−ii−i0000000000
χ30222222-122-2-2-2-2-1-1-12-2-2-1-111-1-11111−2i2i−2i2i00001-1−3−333−3−3330000000000−i3i3−i3i3i−ii−i0000000000
χ312222-2-22222222222-2-2-2-2-22222-2-22200000000-2-200000000222200000000000000-2-200000000
χ322222-2-22222222222-2-2-2-2-22222-2-22200000000-2-200000000-2-2-2-2000000000000002200000000
χ332222-2-2222-2-2-2-2222-222-2-2-2-22222-2-2000000002-20000000000002i2i−2i−2i0000000000000000−2i2i00
χ342222-2-2222-2-2-2-2222-222-2-2-2-22222-2-2000000002-2000000000000−2i−2i2i2i00000000000000002i−2i00
χ352222-2-22-2-2-2-2222222-22-2-2-2-2-2-222222-2-220000-2200000000000000000000002-2-220000000000
χ362222-2-22-2-2-2-2222222-22-2-2-2-2-2-22222-222-20000-220000000000000000000000-222-20000000000
χ372222-2-2-1-2-222-2-2-1-1-122-211-1-11111112i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii000000002-2-1-111−i−iii0000000000
χ382222-2-2-1-2-222-2-2-1-1-122-211-1-11111112i2i−2i−2i−2i−2i2i2i-1-1iiii−i−i−i−i00000000-2211-1-1−i−iii0000000000
χ392222-2-2-1-2-222-2-2-1-1-122-211-1-1111111−2i−2i2i2i2i2i−2i−2i-1-1−i−i−i−iiiii00000000-2211-1-1ii−i−i0000000000
χ402222-2-2-1-2-222-2-2-1-1-122-211-1-1111111−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−i000000002-2-1-111ii−i−i0000000000
χ412222-2-2-1-2-2-2-222-1-1-12-22111111-1-1-1-12-2-2200001-1−i3−i3i3i3i3i3−i3−i30000000000−i3i3i3−i3-111-10000000000
χ422222-2-2-1-2-2-2-222-1-1-12-22111111-1-1-1-12-2-2200001-1i3i3−i3−i3−i3−i3i3i30000000000i3−i3−i3i3-111-10000000000
χ432222-2-2-1-2-2-2-222-1-1-12-22111111-1-1-1-1-222-200001-1−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i31-1-110000000000
χ442222-2-2-1-2-2-2-222-1-1-12-22111111-1-1-1-1-222-200001-1i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i31-1-110000000000
χ4522-2-20022i−2i2-22i−2i2-2-2000002-22i−2i002i−2i00001+i−1−i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i00000000000000001+i−1−i1−i−1+i0000
χ4622-2-20022i−2i2-22i−2i2-2-2000002-22i−2i002i−2i00001+i−1−i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i0000000000000000−1−i1+i−1+i1−i0000
χ4722-2-20022i−2i2-22i−2i2-2-2000002-22i−2i002i−2i0000−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i0000000000000000−1−i1+i−1+i1−i0000
χ4822-2-20022i−2i2-22i−2i2-2-2000002-22i−2i002i−2i0000−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i00000000000000001+i−1−i1−i−1+i0000
χ4922-2-2002−2i2i2-2−2i2i2-2-2000002-2−2i2i00−2i2i00001−i−1+i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i00000000000000001−i−1+i1+i−1−i0000
χ5022-2-2002−2i2i2-2−2i2i2-2-2000002-2−2i2i00−2i2i00001−i−1+i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i0000000000000000−1+i1−i−1−i1+i0000
χ5122-2-2002−2i2i2-2−2i2i2-2-2000002-2−2i2i00−2i2i0000−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i0000000000000000−1+i1−i−1−i1+i0000
χ5222-2-2002−2i2i2-2−2i2i2-2-2000002-2−2i2i00−2i2i0000−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i00000000000000001−i−1+i1+i−1−i0000
χ53444444-2-4-444-4-4-2-2-2-4-44-2-2-2-222-2-2220000000022000000000000000000000000000000000000
χ54444444-2-4-4-4-444-2-2-2-44-4-2-2222222-2-200000000-22000000000000000000000000000000000000
χ554444-4-4-2444444-2-2-2-4-4-422-2-2-2-222-2-20000000022000000000000000000000000000000000000
χ564444-4-4-244-4-4-4-4-2-2-2-4442222-2-2-2-22200000000-22000000000000000000000000000000000000
χ5744-4-40044i−4i-44−4i4i4-4-400000-444i−4i00−4i4i0000000000000000000000000000000000000000000000
χ5844-4-4004−4i4i-444i−4i4-4-400000-44−4i4i004i−4i0000000000000000000000000000000000000000000000
χ5944-4-400-24i−4i4-44i−4i-22200000-22−2i2i00−2i2i00002+2i−2−2i2−2i−2+2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000000
χ6044-4-400-24i−4i4-44i−4i-22200000-22−2i2i00−2i2i0000−2−2i2+2i−2+2i2−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000000
χ6144-4-400-24i−4i-44−4i4i-222000002-2−2i2i002i−2i0000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000
χ6244-4-400-24i−4i-44−4i4i-222000002-2−2i2i002i−2i0000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000000000
χ6344-4-400-2−4i4i4-4−4i4i-22200000-222i−2i002i−2i00002−2i−2+2i2+2i−2−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000000
χ6444-4-400-2−4i4i4-4−4i4i-22200000-222i−2i002i−2i0000−2+2i2−2i−2−2i2+2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000000
χ6544-4-400-2−4i4i-444i−4i-222000002-22i−2i00−2i2i0000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000
χ6644-4-400-2−4i4i-444i−4i-222000002-22i−2i00−2i2i0000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000
χ674-44-44-44000000-4-440004-4000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ684-44-44-44000000-4-440004-40000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ694-44-4-444000000-4-44000-4400000000000000000000000000000022−22−222200000000000000000000
χ704-44-4-444000000-4-44000-44000000000000000000000000000000−222222−2200000000000000000000
χ718-88-88-8-400000044-4000-44000000000000000000000000000000000000000000000000000000
χ728-88-8-88-400000044-40004-4000000000000000000000000000000000000000000000000000000
χ738-8-88008000000-88-800000000000000000000000000000000000000000000000000000000000
χ748-8-8800-40000004-4400000000043−43000000000000000000000000000000000000000000000000
χ758-8-8800-40000004-44000000000−4343000000000000000000000000000000000000000000000000

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