Finite Group Databasebeta

← Group #10768607

Character table — Group #10768607

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888888888888888816161616242424242424242448484848
order122222344666121212124444466121212121212222444446666888812121212121224242424242424246121212222444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-111
χ41111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1
χ511111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ611111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-111-111-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1111-1-11-1-111
χ91111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111111-1-11-1-1-1-1-11111-1-1-1-111-1-11-11-111-1-11-11-1
χ101111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111111-1-11-1-1-1-1-11111-1-1-1-111-1-1-11-11-1-111-11-11
χ111111111-1-1111-1-1-1-1-1-1-11111-1-1-1-11111-11-1-11-11111-1-1111-1-1-1-1-1-1-1-1-11111-1-1111-1-11-11-11-111-1
χ121111111-1-1111-1-1-1-1-1-1-11111-1-1-1-11111-11-1-11-11111-1-1111-1-1-1-1-1-1-1-1-11111-1-111-111-11-11-11-1-11
χ131111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-1-11-111-11-1-1-1-1-1-1111-11111-1-1-1-1111111-1-11-11-111-1-1-11-11
χ141111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-1-11-111-11-1-1-1-1-1-1111-11111-1-1-1-1111111-1-1-11-11-1-1111-11-1
χ151111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-111-1-11-111111111-1-1-1-1-1-1111-1-11-11-111-1-11
χ161111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-111-1-11-111111111-1-1-1-1-1-111-111-11-11-1-111-1
χ1722222222222222222-2-2-2-222-2-222-2-20000000000000000-2-20000000000000000002-2-20020000
χ1822222222222222222-2-2-2-222-2-222-2-20000000000000000-2-2000000000000000000-22200-20000
χ192222222-2-2222-2-2-2-2-222-2-22222-2-2-2-20000000000000000-2200000000000000000022-200-20000
χ202222222-2-2222-2-2-2-2-222-2-22222-2-2-2-20000000000000000-22000000000000000000-2-220020000
χ21222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111111111000000000000
χ23222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-222-2-2221111-2-2-2-2-1-1111111111111-1-1-1-1000000000000
χ24222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-11111000000000000
χ25222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1222-2-2-2-22-1-1-1-122-2-2-111111-1-1-1-11111-1-111000000000000
χ26222222-1-2-2-1-1-11111-2-2-222-1-11111-1-122-22-2-22-2-1-1-1-1-2-222-1111111111-1-1-1-111-1-1000000000000
χ27222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1-2-22-222-221111-2-222-11-1-1-1-11111-1-1-1-1-1-111000000000000
χ28222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1-2-2-22222-2111122-2-2-11-1-1-1-1-1-1-1-1111111-1-1000000000000
χ292222-2-22222222222-22-22-2-2-222-2-222002-2002-200000000-2-20000000000002-2-22000000000000
χ302222-2-22222222222-22-22-2-2-222-2-22200-2200-2200000000-2-2000000000000-222-2000000000000
χ312222-2-22222222222-2-22-22-2-2-2-2-2-2-2-200000000000000002200000000000000002-2000-2200000
χ322222-2-22222222222-2-22-22-2-2-2-2-2-2-2-20000000000000000220000000000000000-220002-200000
χ332222-2-22-2-2222-2-2-2-222-2-22-2-22222-2-200000000000000002-2000000000000000022000-2-200000
χ342222-2-22-2-2222-2-2-2-222-2-22-2-22222-2-200000000000000002-20000000000000000-2-20002200000
χ352222-2-22-2-2222-2-2-2-22-222-2-2-2-2-22222002200-2-200000000-220000000000002-22-2000000000000
χ362222-2-22-2-2222-2-2-2-22-222-2-2-2-2-2222200-2-2002200000000-22000000000000-22-22000000000000
χ372222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-1002-2002-2−i3−i3i3i3000011−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-111-1000000000000
χ382222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-1002-2002-2i3i3−i3−i3000011i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-111-1000000000000
χ392222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-100-2200-22−i3−i3i3i3000011−i3−i3i3i3i3i3−i3−i3i3i3−i3−i31-1-11000000000000
χ402222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-100-2200-22i3i3−i3−i3000011i3i3−i3−i3−i3−i3i3i3−i3−i3i3i31-1-11000000000000
χ412222-2-2-1-2-2-1-1-111112-222-21111-1-1-1-1002200-2-2−i3−i3i3i300001-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-11-11000000000000
χ422222-2-2-1-2-2-1-1-111112-222-21111-1-1-1-1002200-2-2i3i3−i3−i300001-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-11-11000000000000
χ432222-2-2-1-2-2-1-1-111112-222-21111-1-1-1-100-2-20022−i3−i3i3i300001-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i31-11-1000000000000
χ442222-2-2-1-2-2-1-1-111112-222-21111-1-1-1-100-2-20022i3i3−i3−i300001-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i31-11-1000000000000
χ45444444-244-2-2-2-2-2-2-24-4-4-4-4-2-222-2-2220000000000000000220000000000000000000000000000
χ46444444-2-4-4-2-2-22222-444-4-4-2-2-2-2222200000000000000002-20000000000000000000000000000
χ474444-4-4-244-2-2-2-2-2-2-2-4-44-44222222220000000000000000-2-20000000000000000000000000000
χ484444-4-4-2-4-4-2-2-2222244-4-4422-2-2-2-2220000000000000000-220000000000000000000000000000
χ4944-4-40044i−4i4-4-44i4i−4i−4i00000000000002-2002i−2i002-22-20000002i−2i2i−2i000000000000000000000000
χ5044-4-40044i−4i4-4-44i4i−4i−4i0000000000000-2200−2i2i00-22-22000000−2i2i−2i2i000000000000000000000000
χ5144-4-4004−4i4i4-4-4−4i−4i4i4i00000000000002-200−2i2i002-22-2000000−2i2i−2i2i000000000000000000000000
χ5244-4-4004−4i4i4-4-4−4i−4i4i4i0000000000000-22002i−2i00-22-220000002i−2i2i−2i000000000000000000000000
χ5344-4-400-24i−4i-222−2i−2i2i2i000000023−2300−2i32i32-2002i−2i00−1−i31+i3−1+i31−i30000002ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ5444-4-400-24i−4i-222−2i−2i2i2i000000023−2300−2i32i3-2200−2i2i001+i3−1−i31−i3−1+i3000000−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ5544-4-400-24i−4i-222−2i−2i2i2i0000000−2323002i3−2i32-2002i−2i00−1+i31−i3−1−i31+i30000002ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ5644-4-400-24i−4i-222−2i−2i2i2i0000000−2323002i3−2i3-2200−2i2i001−i3−1+i31+i3−1−i3000000−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ5744-4-400-2−4i4i-2222i2i−2i−2i000000023−23002i3−2i32-200−2i2i00−1+i31−i3−1−i31+i3000000−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ5844-4-400-2−4i4i-2222i2i−2i−2i000000023−23002i3−2i3-22002i−2i001−i3−1+i31+i3−1−i30000002ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ5944-4-400-2−4i4i-2222i2i−2i−2i0000000−232300−2i32i32-200−2i2i00−1−i31+i3−1+i31−i3000000−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ6044-4-400-2−4i4i-2222i2i−2i−2i0000000−232300−2i32i3-22002i−2i001+i3−1−i31−i3−1+i30000002ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ614-4-444-4400-44-40000000004-400000000000000000000−2i22i20000000000−2i22i2−2i22i20000000000000000
χ624-4-444-4400-44-40000000004-4000000000000000000002i2−2i200000000002i2−2i22i2−2i20000000000000000
χ634-4-444-4-2002-2223−2323−2300000-220023−230000000000000000−2i22i2000000i6−i6i6−i6i2−i2i2−i20000000000000000
χ644-4-444-4-2002-2223−2323−2300000-220023−2300000000000000002i2−2i2000000−i6i6−i6i6−i2i2−i2i20000000000000000
χ654-4-444-4-2002-22−2323−232300000-2200−23230000000000000000−2i22i2000000−i6i6−i6i6i2−i2i2−i20000000000000000
χ664-4-444-4-2002-22−2323−232300000-2200−232300000000000000002i2−2i2000000i6−i6i6−i6−i2i2−i2i20000000000000000
χ674-4-44-44400-44-4000000000-4400000000000000000022−220000000022−22−222200000000000000000000
χ684-4-44-44400-44-4000000000-44000000000000000000−222200000000−222222−2200000000000000000000
χ694-4-44-44-2002-2223−2323−23000002-200−23230000000000000022−2200000000−222−26−6−660000000000000000
χ704-4-44-44-2002-2223−2323−23000002-200−232300000000000000−2222000000002−2−22−666−60000000000000000
χ714-4-44-44-2002-22−2323−2323000002-20023−230000000000000022−2200000000−222−2−666−60000000000000000
χ724-4-44-44-2002-22−2323−2323000002-20023−2300000000000000−2222000000002−2−226−6−660000000000000000
χ738-88-800800-8-88000000000000000000000000000000000000000000000000000000000000000
χ748-88-800-40044-4−4i34i34i3−4i300000000000000000000000000000000000000000000000000000000000
χ758-88-800-40044-44i3−4i3−4i34i300000000000000000000000000000000000000000000000000000000000

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