Finite Group Databasebeta

← Group #10846224

Character table — Group #10846224

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order12222234444446664446612121212121212122222444466661212121212128888888866881212242424248888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-111-1-1
χ611111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111
χ711111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1111111-1-1
χ91111111-1-11111111-1-1-111111-1-1-1-11111-1-1-11-11111-1-1-1-1-1-1111111-1-11-11-11-111-1-1-1-1-1-1111-11-1
χ101111111-1-11111111-1-1-111111-1-1-1-11111-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-1111-11-11-111-1-11111-1-1-11-11
χ111111111-1-11111111-1-1-111111-1-1-1-1111-11-1-1-111111-1-1-1-1-1-11111-1-111-11-11-11-1-111-1-1-1-111-11-11
χ121111111-1-11111111-1-1-111111-1-1-1-1111-11-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11-1-1111111-1-11-11-1
χ131111111-1-11111111-1-1-111111-1-1-1-11-1-11-1111-1-1-1-1-1-1-11111111111-1-11-1-111-1-1-111-1-111-1-11-1-11
χ141111111-1-11111111-1-1-111111-1-1-1-11-1-11-1111-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111-1-1-11111-1-111-111-1
χ151111111-1-11111111-1-1-111111-1-1-1-11-1-1-1111-11-1-1-1-1-1-111111111-1-111-111-1-1111-1-1-1-111-1-1-111-1
χ161111111-1-11111111-1-1-111111-1-1-1-11-1-1-1111-11-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-1111-1-111-1-1111-1-11
χ17222222222-2-2-2-2222-2-2222-2-2-22222-2000000000000-2-200002i2i−2i−2i000000000000002i−2i00000000
χ18222222222-2-2-2-2222-2-2222-2-2-22222-2000000000000-2-20000−2i−2i2i2i00000000000000−2i2i00000000
χ192222222-2-2-2-2-2-222222-222-2-2-2-2-2-2-2-20000000000002200002i2i−2i−2i00000000000000−2i2i00000000
χ202222222-2-2-2-2-2-222222-222-2-2-2-2-2-2-2-2000000000000220000−2i−2i2i2i000000000000002i−2i00000000
χ21222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-100000000-1-122-1-1-1-1-1-10000000000
χ22222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-10000000011-2-21111110000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1111100000000-1-1-2-2-1-111110000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1111100000000112211-1-1-1-10000000000
χ25222222-1-2-22222-1-1-1-2-2-2-1-1-1-1-11111-1222-2-2-22-2-1-1-1-111111100000000-112-2-11-1-1110000000000
χ26222222-1-2-22222-1-1-1-2-2-2-1-1-1-1-11111-122-22-2-2-22-1-1-1-1111111000000001-1-221-111-1-10000000000
χ27222222-1-2-22222-1-1-1-2-2-2-1-1-1-1-11111-1-2-22-2222-2111111-1-1-1-100000000-11-22-1111-1-10000000000
χ28222222-1-2-22222-1-1-1-2-2-2-1-1-1-1-11111-1-2-2-2222-22111111-1-1-1-1000000001-12-21-1-1-1110000000000
χ292222-2-22222-22-22222-2-2-2-22-2-222-2-22002-200-2200002-20000000000002-200-2200000000000000
χ302222-2-22222-22-22222-2-2-2-22-2-222-2-2200-22002-200002-2000000000000-22002-200000000000000
χ312222-2-2222-22-22222-22-2-2-2-22222-2-2-2000000000000-220000000022220000000000000000-2-200
χ322222-2-2222-22-22222-22-2-2-2-22222-2-2-2000000000000-2200000000-2-2-2-200000000000000002200
χ332222-2-22-2-22-22-2222-222-2-22-2-2-2-2222002200-2-20000-220000000000002200-2-200000000000000
χ342222-2-22-2-22-22-2222-222-2-22-2-2-2-222200-2-200220000-22000000000000-2-2002200000000000000
χ352222-2-22-2-2-22-222222-22-2-2-222-2-222-20000000000002-20000000022-2-20000000000000000-2200
χ362222-2-22-2-2-22-222222-22-2-2-222-2-222-20000000000002-200000000-2-22200000000000000002-200
χ372222-2-2-1222-22-2-1-1-12-2-211-111-1-111-1002-200-22−i3−i3i3i3-11−i3−i3i3i300000000-11001-1−i3i3−i3i30000000000
χ382222-2-2-1222-22-2-1-1-12-2-211-111-1-111-1002-200-22i3i3−i3−i3-11i3i3−i3−i300000000-11001-1i3−i3i3−i30000000000
χ392222-2-2-1222-22-2-1-1-12-2-211-111-1-111-100-22002-2−i3−i3i3i3-11−i3−i3i3i3000000001-100-11i3−i3i3−i30000000000
χ402222-2-2-1222-22-2-1-1-12-2-211-111-1-111-100-22002-2i3i3−i3−i3-11i3i3−i3−i3000000001-100-11−i3i3−i3i30000000000
χ412222-2-2-1-2-22-22-2-1-1-1-22211-11111-1-1-1002200-2-2−i3−i3i3i31-1i3i3−i3−i300000000-1-10011−i3i3i3−i30000000000
χ422222-2-2-1-2-22-22-2-1-1-1-22211-11111-1-1-1002200-2-2i3i3−i3−i31-1−i3−i3i3i300000000-1-10011i3−i3−i3i30000000000
χ432222-2-2-1-2-22-22-2-1-1-1-22211-11111-1-1-100-2-20022−i3−i3i3i31-1i3i3−i3−i3000000001100-1-1i3−i3−i3i30000000000
χ442222-2-2-1-2-22-22-2-1-1-1-22211-11111-1-1-100-2-20022i3i3−i3−i31-1−i3−i3i3i3000000001100-1-1−i3i3i3−i30000000000
χ452-2-222-220022-2-2-22-20002-222-20000-200002i−2i000000002i−2i2i−2i2i−2i2i−2i00000000000000002-2000000
χ462-2-222-220022-2-2-22-20002-222-20000-200002i−2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000-22000000
χ472-2-222-220022-2-2-22-20002-222-20000-20000−2i2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000-22000000
χ482-2-222-220022-2-2-22-20002-222-20000-20000−2i2i00000000−2i2i−2i2i−2i2i−2i2i00000000000000002-2000000
χ492-2-222-2200-2-222-22-20002-2-2-22000022-20000002-22-20000002-2-220000000000000000002-20000
χ502-2-222-2200-2-222-22-20002-2-2-22000022-20000002-22-2000000-222-2000000000000000000-220000
χ512-2-222-2200-2-222-22-20002-2-2-2200002-22000000-22-220000002-2-22000000000000000000-220000
χ522-2-222-2200-2-222-22-20002-2-2-2200002-22000000-22-22000000-222-20000000000000000002-20000
χ53444444-244-4-4-4-4-2-2-2-4-44-2-2222-2-2-2-220000000000002200000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-244-4-2-222222222000000000000-2-200000000000000000000000000000000
χ554444-4-4-244-44-44-2-2-2-44-4222-2-2-2-22220000000000002-200000000000000000000000000000000
χ564444-4-4-2-4-4-44-44-2-2-24-44222-2-222-2-22000000000000-2200000000000000000000000000000000
χ5744-4-40044i−4i00004-4-4000000004i−4i000000000000000000000000022−22−2i22i200000000000000000000
χ5844-4-40044i−4i00004-4-4000000004i−4i0000000000000000000000000−22222i2−2i200000000000000000000
χ5944-4-4004−4i4i00004-4-400000000−4i4i000000000000000000000000022−222i2−2i200000000000000000000
χ6044-4-4004−4i4i00004-4-400000000−4i4i0000000000000000000000000−2222−2i22i200000000000000000000
χ614-4-444-4-20044-4-42-22000-22-2-220000200004i−4i00000000−2i2i−2i2i0000000000000000000000000000
χ624-4-444-4-20044-4-42-22000-22-2-22000020000−4i4i000000002i−2i2i−2i0000000000000000000000000000
χ634-4-444-4-200-4-4442-22000-2222-20000-24-4000000-22-220000000000000000000000000000000000
χ644-4-444-4-200-4-4442-22000-2222-20000-2-440000002-22-20000000000000000000000000000000000
χ654-4-44-444004-4-44-44-4000-444-440000-40000000000000000000000000000000000000000000000
χ664-4-44-44400-444-4-44-4000-44-44-4000040000000000000000000000000000000000000000000000
χ674-4-44-44-2004-4-442-220002-2-22-2000020000000000000023−23−23230000000000000000000000000000
χ684-4-44-44-2004-4-442-220002-2-22-20000200000000000000−232323−230000000000000000000000000000
χ694-4-44-44-200-444-42-220002-22-220000-200000000−2i32i32i3−2i30000000000000000000000000000000000
χ704-4-44-44-200-444-42-220002-22-220000-2000000002i3−2i3−2i32i30000000000000000000000000000000000
χ7188-8-800-48i−8i0000-44400000000−4i4i0000000000000000000000000000000000000000000000000
χ7288-8-800-4−8i8i0000-444000000004i−4i0000000000000000000000000000000000000000000000000
χ738-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-88-800-400000044-40000000000−4i34i300000000000000000000000000000000000000000000000
χ758-88-800-400000044-400000000004i3−4i300000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).