Finite Group Databasebeta

← Group #10780325

Character table — Group #10780325

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881212121216161616161616161616161624242424242448484848
order12223444466624444668888121212121212121288121224242424242424248888448812121212242424242444882488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-111
χ71111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ81111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1
χ9111111111111-1-11-1-1-1-111111-1-1-1-1111-1-1-111111-1-1-1-111-1-11-11-111-1-111-1-11-1-111-11-11-1
χ10111111111111-1-11-1-1-1-111111-1-1-1-1111-1-1-111111-1-1-1-111-1-1-11-11-1-111-1-1111-1-111-1-11-11
χ11111111111111-1-11-1-1-1-111111-1-1-1-1111-1-1-111111-1-1-1-1-1-1111-11-111-1-111-1-1-111-1-11-11-11
χ12111111111111-1-11-1-1-1-111111-1-1-1-1111-1-1-111111-1-1-1-1-1-111-11-11-1-111-1-111-111-1-111-11-1
χ13111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-111111-11-1-1-1-1111111-1-11-1-1111-1-1-1-111-111-11-11-1-11
χ14111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-111111-11-1-1-1-1111111-1-1-111-1-1-11111-1-1-111-11-1-111-1
χ15111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-111111-11-1-1-1-11111-1-1111-1-1111-1-1-1-1111-1-11-11-111-1
χ16111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-111111-11-1-1-1-11111-1-111-111-1-1-11111-1-11-1-11-111-1-11
χ17222222-2-2222222-2-2-2220000222-2-2-2-2200-2-20000000000000000000000002-22-2000000
χ18222222-2-2222222-2-2-2220000222-2-2-2-2200-2-2000000000000000000000000-22-22000000
χ19222222-2-22222-2-2-222-2-200002-2-222-2-22002-200000000000000000000000022-2-2000000
χ20222222-2-22222-2-2-222-2-200002-2-222-2-22002-2000000000000000000000000-2-222000000
χ2122222-222-22222-2-2-22220000-2-2-2-2-222-2002-20000000022-2-20000000000000000-220000
χ2222222-222-22222-2-2-22220000-2-2-2-2-222-2002-200000000-2-22200000000000000002-20000
χ2322222-222-2222-22-22-2-2-20000-2222222-200-2-20000000022220000000000000000-2-20000
χ2422222-222-2222-22-22-2-2-20000-2222222-200-2-200000000-2-2-2-20000000000000000220000
χ2522222-2-2-2-22222-222-2222i2i−2i−2i-2-2-222-2-2-22i−2i-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ2622222-2-2-2-22222-222-222−2i−2i2i2i-2-2-222-2-2-2−2i2i-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ2722222-2-2-2-2222-222-22-2-22i2i−2i−2i-222-2-2-2-2-2−2i2i222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ2822222-2-2-2-2222-222-22-2-2−2i−2i2i2i-222-2-2-2-2-22i−2i22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ292222-12222-1-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-10000000000
χ302222-12222-1-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2111111110000000000
χ312222-12222-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-111111111000022-2-2-1-1-1-111110000000000
χ322222-12222-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2221111-1-1-1-10000000000
χ332222-12222-1-1-1-2-22-2-2112222-11111-1-1-1-2-21-1-1-1-1-1111100002-22-2-1-111-1-1110000000000
χ342222-12222-1-1-1-2-22-2-2112222-11111-1-1-1-2-21-1-1-1-1-111110000-22-2211-1-111-1-10000000000
χ352222-12222-1-1-1-2-22-2-211-2-2-2-2-11111-1-1-1221-11111-1-1-1-100002-2-22-1-11111-1-10000000000
χ362222-12222-1-1-1-2-22-2-211-2-2-2-2-11111-1-1-1221-11111-1-1-1-10000-222-211-1-1-1-1110000000000
χ372222-1-2-2-2-2-1-1-12-222-2-1-12i2i−2i−2i111-1-11112i−2i1-1−i−iii−i−iii00000000−i3i3−i3i33−33−30000000000
χ382222-1-2-2-2-2-1-1-12-222-2-1-12i2i−2i−2i111-1-11112i−2i1-1−i−iii−i−iii00000000i3−i3i3−i3−33−330000000000
χ392222-1-2-2-2-2-1-1-12-222-2-1-1−2i−2i2i2i111-1-1111−2i2i1-1ii−i−iii−i−i00000000−i3i3−i3i3−33−330000000000
χ402222-1-2-2-2-2-1-1-12-222-2-1-1−2i−2i2i2i111-1-1111−2i2i1-1ii−i−iii−i−i00000000i3−i3i3−i33−33−30000000000
χ412222-1-2-2-2-2-1-1-1-222-22112i2i−2i−2i1-1-111111−2i2i-1-1−i−iiiii−i−i00000000−i3i3i3−i33−3−330000000000
χ422222-1-2-2-2-2-1-1-1-222-22112i2i−2i−2i1-1-111111−2i2i-1-1−i−iiiii−i−i00000000i3−i3−i3i3−333−30000000000
χ432222-1-2-2-2-2-1-1-1-222-2211−2i−2i2i2i1-1-1111112i−2i-1-1ii−i−i−i−iii00000000−i3i3i3−i3−333−30000000000
χ442222-1-2-2-2-2-1-1-1-222-2211−2i−2i2i2i1-1-1111112i−2i-1-1ii−i−i−i−iii00000000i3−i3−i3i33−3−330000000000
χ454444-24-4-44-2-2-244-4-4-4-2-20000-2-2-22222-200220000000000000000000000000000000000
χ464444-24-4-44-2-2-2-4-4-444220000-222-2-222-200-220000000000000000000000000000000000
χ474444-2-444-4-2-2-24-4-4-44-2-2000022222-2-2200-220000000000000000000000000000000000
χ484444-2-444-4-2-2-2-44-44-42200002-2-2-2-2-2-2200220000000000000000000000000000000000
χ4944-4-44400-44-4-4000000022−2222−224000000-4000022−2222−22000000000000000000000000000000
χ5044-4-44400-44-4-40000000−2222−22224000000-40000−2222−2222000000000000000000000000000000
χ5144-4-44-40044-4-40000000−2i22i22i2−2i2-400000040000−2i22i22i2−2i2000000000000000000000000000000
χ5244-4-44-40044-4-400000002i2−2i2−2i22i2-4000000400002i2−2i2−2i22i2000000000000000000000000000000
χ5344-4-4-2400-4-22200000−2i32i322−2222−22-2−2i32i3000020000−22−22i6−i6i6−i600000000000000000000000000
χ5444-4-4-2400-4-22200000−2i32i3−2222−2222-2−2i32i30000200002−22−2−i6i6−i6i600000000000000000000000000
χ5544-4-4-2400-4-222000002i3−2i322−2222−22-22i3−2i3000020000−22−22−i6i6−i6i600000000000000000000000000
χ5644-4-4-2400-4-222000002i3−2i3−2222−2222-22i3−2i30000200002−22−2i6−i6i6−i600000000000000000000000000
χ5744-4-4-2-4004-22200000−2i32i3−2i22i22i2−2i222i3−2i30000-20000i2−i2−i2i26−6−6600000000000000000000000000
χ5844-4-4-2-4004-22200000−2i32i32i2−2i2−2i22i222i3−2i30000-20000−i2i2i2−i2−666−600000000000000000000000000
χ5944-4-4-2-4004-222000002i3−2i3−2i22i22i2−2i22−2i32i30000-20000i2−i2−i2i2−666−600000000000000000000000000
χ6044-4-4-2-4004-222000002i3−2i32i2−2i2−2i22i22−2i32i30000-20000−i2i2i2−i26−6−6600000000000000000000000000
χ614-4-44404-40-44-400000000000000004-40000000000000004i−4i0000000000000000000000
χ624-4-44404-40-44-400000000000000004-4000000000000000−4i4i0000000000000000000000
χ634-4-4440-440-44-40000000000000000-4400000000000004i−4i000000000000000000000000
χ644-4-4440-440-44-40000000000000000-440000000000000−4i4i000000000000000000000000
χ658-88-880000-8-88000000000000000000000000000000000000000000000000000000000
χ668-88-8-4000044-400000000000000−4i34i300000000000000000000000000000000000000000
χ678-88-8-4000044-4000000000000004i3−4i300000000000000000000000000000000000000000
χ688-8-88-408-804-440000000000000000-44000000000000000000000000000000000000000
χ698-8-88-40-8804-4400000000000000004-4000000000000000000000000000000000000000

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