Finite Group Databasebeta

← Group #10767964

Character table — Group #10767964

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order122222344446664444661212121212121212224444441212121212121212121222226688121224242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-11-1-1-1-11-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1111111-1-1
χ91111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-1111-1-1-111111-1-1-1-1-111-1-11-11-11-111-1-11-11-11-111-1-11-1
χ101111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-1111-1-1-111111-1-1-1-1-1-1-1111-11-11-111-1-1-11-11-11-1-111-11
χ111111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-1-1-11-1111-1-1-1-1-1111111-1-11-1-111-1-1-1111-11-11-1-1-111-11
χ121111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-1-1-11-1111-1-1-1-1-11111-1-1111-1-111-1-1-111-11-11-1111-1-11-1
χ131111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1111-11-1-111111-1-1-1-1-111-1-1-11-11-11-1-111-111-1-1111-1-1-11
χ141111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1111-11-1-111111-1-1-1-1-1-1-111-11-11-11-1-1111-1-111-1-1-1111-1
χ151111111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-1-1-11111-1-1-1-1-1111111-1-1-111-1-1111-1-1-111-1-11-1-1111-1
χ161111111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-1-1-11111-1-1-1-1-11111-1-111-111-1-1111-1-11-1-111-111-1-1-11
χ1722222222222222-2-2-2-2222222-2-2-2-200000000-20000-2000022-2-2000000000000-2200000000
χ1822222222222222-2-2-2-2222222-2-2-2-200000000-20000-20000-2-2220000000000002-200000000
χ192222222-2-2-2-222222-2-222-2-2-2-222-2-200000000-20000200002222000000000000-2-200000000
χ202222222-2-2-2-222222-2-222-2-2-2-222-2-200000000-2000020000-2-2-2-20000000000002200000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-1-122-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122-2-222-2-2-11111-111110000-1-1-2-2-1-11111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-1-1-1-1-1-1000011-2-2111111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-11111-111110000112211-1-1-1-1000000000000
χ25222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-12-2222-2-2-2-1-1-1-1-1111110000-112-2-11-1-111000000000000
χ26222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-12-2-2-22-222-111111-1-1-1-10000-11-22-1111-1-1000000000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2222-22-2-2-1-1-1-1-11111100001-1-221-111-1-1000000000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-22-2-2-2222-111111-1-1-1-100001-12-21-1-1-111000000000000
χ292222-2-2222-2-22222-22-2-2-222-2-222222-200-2200-20000-2000000002-200-220000000000000000
χ302222-2-2222-2-22222-22-2-2-222-2-22222-22002-200-20000-200000000-22002-20000000000000000
χ312222-2-2222-2-2222-22-22-2-222-2-2-2-2-2-2000000002000020000000000000000002-200-22000000
χ322222-2-2222-2-2222-22-22-2-222-2-2-2-2-2-200000000200002000000000000000000-22002-2000000
χ332222-2-22-2-2222222-2-22-2-2-2-22222-2-20000000020000-20000000000000000002200-2-2000000
χ342222-2-22-2-2222222-2-22-2-2-2-22222-2-20000000020000-2000000000000000000-2-20022000000
χ352222-2-22-2-222222-222-2-2-2-2-222-2-2222200-2-200-200002000000002200-2-20000000000000000
χ362222-2-22-2-222222-222-2-2-2-2-222-2-222-2-2002200-20000200000000-2-200220000000000000000
χ372222-2-2-122-2-2-1-1-12-22-211-1-111-1-1-1-12-200-22001−i3−i3i3i31−i3−i3i3i30000-11001-1−i3i3−i3i3000000000000
χ382222-2-2-122-2-2-1-1-12-22-211-1-111-1-1-1-12-200-22001i3i3−i3−i31i3i3−i3−i30000-11001-1i3−i3i3−i3000000000000
χ392222-2-2-122-2-2-1-1-12-22-211-1-111-1-1-1-1-22002-2001−i3−i3i3i31−i3−i3i3i300001-100-11i3−i3i3−i3000000000000
χ402222-2-2-122-2-2-1-1-12-22-211-1-111-1-1-1-1-22002-2001i3i3−i3−i31i3i3−i3−i300001-100-11−i3i3−i3i3000000000000
χ412222-2-2-1-2-222-1-1-1-222-21111-1-111-1-12200-2-2001−i3−i3i3i3-1i3i3−i3−i30000-1-10011−i3i3i3−i3000000000000
χ422222-2-2-1-2-222-1-1-1-222-21111-1-111-1-12200-2-2001i3i3−i3−i3-1−i3−i3i3i30000-1-10011i3−i3−i3i3000000000000
χ432222-2-2-1-2-222-1-1-1-222-21111-1-111-1-1-2-20022001−i3−i3i3i3-1i3i3−i3−i300001100-1-1i3−i3−i3i3000000000000
χ442222-2-2-1-2-222-1-1-1-222-21111-1-111-1-1-2-20022001i3i3−i3−i3-1−i3−i3i3i300001100-1-1−i3i3i3−i3000000000000
χ45444444-24444-2-2-2-4-4-4-4-2-2-2-2-2-2222200000000200002000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-244-4-4-2-22222-2-2220000000020000-2000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-2-44-4422-2-222222200000000-20000-2000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-24-4-442222-2-2-2-22200000000-200002000000000000000000000000000000
χ4944-4-40044i−4i00-44-40000004i−4i000000002-2002i−2i02-22-202i−2i2i−2i00000000000000000000000000
χ5044-4-40044i−4i00-44-40000004i−4i00000000-2200−2i2i0-22-220−2i2i−2i2i00000000000000000000000000
χ5144-4-4004−4i4i00-44-4000000−4i4i000000002-200−2i2i02-22-20−2i2i−2i2i00000000000000000000000000
χ5244-4-4004−4i4i00-44-4000000−4i4i00000000-22002i−2i0-22-2202i−2i2i−2i00000000000000000000000000
χ5344-4-400-24i−4i002-22000000−2i2i0023−23−2i32i3002-2002i−2i0−1−i31+i3−1+i31−i302ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ5444-4-400-24i−4i002-22000000−2i2i0023−23−2i32i300-2200−2i2i01+i3−1−i31−i3−1+i30−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ5544-4-400-24i−4i002-22000000−2i2i00−23232i3−2i3002-2002i−2i0−1+i31−i3−1−i31+i302ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ5644-4-400-24i−4i002-22000000−2i2i00−23232i3−2i300-2200−2i2i01−i3−1+i31+i3−1−i30−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ5744-4-400-2−4i4i002-220000002i−2i0023−232i3−2i3002-200−2i2i0−1+i31−i3−1−i31+i30−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ5844-4-400-2−4i4i002-220000002i−2i0023−232i3−2i300-22002i−2i01−i3−1+i31+i3−1−i302ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ5944-4-400-2−4i4i002-220000002i−2i00−2323−2i32i3002-200−2i2i0−1−i31+i3−1+i31−i30−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ6044-4-400-2−4i4i002-220000002i−2i00−2323−2i32i300-22002i−2i01+i3−1−i31−i3−1+i302ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ614-44-4004004-44-4-4000000004-40000000000000000000000000000000000000000002i−2i2i−2i00
χ624-44-4004004-44-4-4000000004-4000000000000000000000000000000000000000000−2i2i−2i2i00
χ634-44-400400-444-4-400000000-440000000000000000000000000000000000000000002i−2i−2i2i00
χ644-44-400400-444-4-400000000-44000000000000000000000000000000000000000000−2i2i2i−2i00
χ654-4-444-440000-4-4400004-400000000000000000000000000004-40000000000000000000000
χ664-4-444-440000-4-4400004-40000000000000000000000000000-440000000000000000000000
χ674-4-44-4440000-4-440000-44000000000000000000000000004-4000000000000000000000000
χ684-4-44-4440000-4-440000-4400000000000000000000000000-44000000000000000000000000
χ698-88-800-4008-8-44400000000-44000000000000000000000000000000000000000000000000
χ708-88-800-400-88-444000000004-4000000000000000000000000000000000000000000000000
χ718-8-888-8-4000044-40000-440000000000000000000000000000000000000000000000000000
χ728-8-88-88-4000044-400004-40000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.