Finite Group Databasebeta

← Group #10692057

Character table — Group #10692057

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order122222344444466666664441212121212121212444488881212121212121212121224242424242424244412121212244488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ91111-1-111-1-1-11-1-1-111-1-1111-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i1-1iiii−i−i−i−i1-111-1-11-1-11i−ii−ii−i1-1
χ101111-1-111-1-1-11-1-1-111-1-1111-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i1-1iiii−i−i−i−i1-111-1-1-111-1−ii−ii−ii-11
χ111111-1-111-1-1-11-1-1-111-1-1111-11111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i1-1−i−i−i−iiiii-11-1-1111-1-11−ii−iii−i-11
χ121111-1-111-1-1-11-1-1-111-1-1111-11111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i1-1−i−i−i−iiiii-11-1-111-111-1i−ii−i−ii1-1
χ131111-1-111-1-1-11-1-1-111-1-1111-11111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiii1-1iiii−i−i−i−i-11-1-1111-1-11i−ii−i−ii-11
χ141111-1-111-1-1-11-1-1-111-1-1111-11111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiii1-1iiii−i−i−i−i-11-1-111-111-1−ii−iii−i1-1
χ151111-1-111-1-1-11-1-1-111-1-1111-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii1-1−i−i−i−iiiii1-111-1-11-1-11−ii−ii−ii1-1
χ161111-1-111-1-1-11-1-1-111-1-1111-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii1-1−i−i−i−iiiii1-111-1-1-111-1i−ii−ii−i-11
χ17222222222-2-2222222222-2-2-222-2-222-2-20000000000000000-2-20000000000000022-2-200000000
χ18222222222-2-2222222222-2-2-222-2-222-2-20000000000000000-2-200000000000000-2-22200000000
χ192222222-2-222-2-222222222-2-2-2-222-2-22200002-22-200000000-2-222-2-222-2-2000000000000000000
χ202222222-2-222-2-222222222-2-2-2-222-2-2220000-22-2200000000-2-2-2-222-2-222000000000000000000
χ212222222-2-2-2-2-2-22222222-222-2-2-2-2-2-2-2-20000000000000000220000000000000000002i−2i−2i2i0000
χ222222222-2-2-2-2-2-22222222-222-2-2-2-2-2-2-2-2000000000000000022000000000000000000−2i2i2i−2i0000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ25222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-2-21111000000000000
χ26222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-11111111122-1-1-1-1000000000000
χ27222222-1-2-222-2-2-1-1-1-1-1-1-12-2-211-1-111-1-100002-22-2−i3−i3i3i3−i3−i3i3i311-1-111-1-11100−i3i3−i3i3000000000000
χ28222222-1-2-222-2-2-1-1-1-1-1-1-12-2-211-1-111-1-100002-22-2i3i3−i3−i3i3i3−i3−i311-1-111-1-11100i3−i3i3−i3000000000000
χ29222222-1-2-222-2-2-1-1-1-1-1-1-12-2-211-1-111-1-10000-22-22−i3−i3i3i3−i3−i3i3i31111-1-111-1-100i3−i3i3−i3000000000000
χ30222222-1-2-222-2-2-1-1-1-1-1-1-12-2-211-1-111-1-10000-22-22i3i3−i3−i3i3i3−i3−i31111-1-111-1-100−i3i3−i3i3000000000000
χ312222-2-222-2222-2-2-222-2-22-2-2222-2-2-2-2220000000000000000-22000000000000002-22-200000000
χ322222-2-222-2222-2-2-222-2-22-2-2222-2-2-2-2220000000000000000-2200000000000000-22-2200000000
χ332222-2-22-2222-22-2-222-2-22-22-2-2-2-2-2222200000000000000002-200000000000000000022-2-20000
χ342222-2-22-2222-22-2-222-2-22-22-2-2-2-2-2222200000000000000002-2000000000000000000-2-2220000
χ352222-2-22-22-2-2-22-2-222-2-222-22-2-22222-2-200002i−2i−2i2i00000000-222i2i−2i−2i−2i−2i2i2i000000000000000000
χ362222-2-22-22-2-2-22-2-222-2-222-22-2-22222-2-20000−2i2i2i−2i00000000-22−2i−2i2i2i2i2i−2i−2i000000000000000000
χ372222-2-2-12-2-2-22-211-1-111-122-2-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii-11−i−i−i−iiiii2-2-1-111000000000000
χ382222-2-2-12-2-2-22-211-1-111-122-2-1-1-1-111112i2i−2i−2i−2i−2i2i2i−i−i−i−iiiii-11iiii−i−i−i−i-2211-1-1000000000000
χ392222-2-2-12-2-2-22-211-1-111-122-2-1-1-1-11111−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i-11−i−i−i−iiiii-2211-1-1000000000000
χ402222-2-2-12-2-2-22-211-1-111-122-2-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i-11iiii−i−i−i−i2-2-1-111000000000000
χ412222-2-2-1-22-2-2-2211-1-111-12-2211-1-1-1-11100002i−2i−2i2i33−3−3−3−3331-1−i−iiiii−i−i00−i3i3i3−i3000000000000
χ422222-2-2-1-22-2-2-2211-1-111-12-2211-1-1-1-11100002i−2i−2i2i−3−33333−3−31-1−i−iiiii−i−i00i3−i3−i3i3000000000000
χ432222-2-2-1-22-2-2-2211-1-111-12-2211-1-1-1-1110000−2i2i2i−2i33−3−3−3−3331-1ii−i−i−i−iii00i3−i3−i3i3000000000000
χ442222-2-2-1-22-2-2-2211-1-111-12-2211-1-1-1-1110000−2i2i2i−2i−3−33333−3−31-1ii−i−i−i−iii00−i3i3i3−i3000000000000
χ45444444-244-4-444-2-2-2-2-2-2-2-4-4-4-2-222-2-22200000000000000002200000000000000000000000000
χ46444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2-444222222220000000000000000-2-200000000000000000000000000
χ474444-4-4-24-4444-422-2-222-2-4-44-2-22222-2-200000000000000002-200000000000000000000000000
χ484444-4-4-2-4444-4422-2-222-2-44-42222-2-2-2-20000000000000000-2200000000000000000000000000
χ4944-4-4004004-400004-400-40000000004-42-22-200002-22-22-22-20000000000000000000000000000
χ5044-4-4004004-400004-400-40000000004-4-22-220000-22-22-22-220000000000000000000000000000
χ5144-4-400400-4400004-400-4000000000-442i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ5244-4-400400-4400004-400-4000000000-44−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ5344-4-400-2004-400−2i32i3-22−2i32i3200000−2i32i300-222-22-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000000000000000
χ5444-4-400-2004-400−2i32i3-22−2i32i3200000−2i32i300-22-22-2200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000000000000000
χ5544-4-400-2004-4002i3−2i3-222i3−2i32000002i3−2i300-222-22-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000000000000000
χ5644-4-400-2004-4002i3−2i3-222i3−2i32000002i3−2i300-22-22-2200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000000000000000
χ5744-4-400-200-4400−2i32i3-22−2i32i32000002i3−2i3002-22i−2i−2i2i00002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ220000000000000000000000000000
χ5844-4-400-200-4400−2i32i3-22−2i32i32000002i3−2i3002-2−2i2i2i−2i0000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ220000000000000000000000000000
χ5944-4-400-200-44002i3−2i3-222i3−2i3200000−2i32i3002-22i−2i−2i2i00002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ140000000000000000000000000000
χ6044-4-400-200-44002i3−2i3-222i3−2i3200000−2i32i3002-2−2i2i2i−2i0000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ140000000000000000000000000000
χ614-44-44-444-400-4444-44-4-4-40004-4004-40000000000000000000000000000000000000000000000
χ624-44-44-44-44004-444-44-4-4-4000-4400-440000000000000000000000000000000000000000000000
χ634-44-44-4-24-400-44-2-22-2222000-2200-2200000000000000000000i6−i6i6−i6i6−i6i6−i6000000000000000000
χ644-44-44-4-24-400-44-2-22-2222000-2200-2200000000000000000000−i6i6−i6i6−i6i6−i6i6000000000000000000
χ654-44-44-4-2-44004-4-2-22-22220002-2002-200000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000
χ664-44-44-4-2-44004-4-2-22-22220002-2002-200000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000
χ674-44-4-4444400-4-4-4-4-4444-40004-400-440000000000000000000000000000000000000000000000
χ684-44-4-444-4-40044-4-4-4444-4000-44004-40000000000000000000000000000000000000000000000
χ694-44-4-44-24400-4-4222-2-2-22000-22002-2000000000000000000006−66−6−66−66000000000000000000
χ704-44-4-44-24400-4-4222-2-2-22000-22002-200000000000000000000−66−666−66−6000000000000000000
χ714-44-4-44-2-4-40044222-2-2-220002-200-22000000000000000000006−6−66−666−6000000000000000000
χ724-44-4-44-2-4-40044222-2-2-220002-200-2200000000000000000000−666−66−6−66000000000000000000
χ738-8-8800800000000-8-80080000000000000000000000000000000000000000000000000000000
χ748-8-8800-4000000−4i34i3444i3−4i3-40000000000000000000000000000000000000000000000000000000
χ758-8-8800-40000004i3−4i344−4i34i3-40000000000000000000000000000000000000000000000000000000

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