Finite Group Databasebeta

← Group #10780317

Character table — Group #10780317

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881212121216161616161616161616161624242424242448484848
order1222344446662444488881212121212121212121268812242424242424242488882466881212242424242444884488
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
χ511111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111
χ711111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ811111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1
χ9111111111111-1-1-11-11111-1-1-1-1-1-11111-1-1-111111-1-1-1-111-1-11-1111-1-1-111-1-11-11-11-11-11-1
χ10111111111111-1-1-11-11111-1-1-1-1-1-11111-1-1-111111-1-1-1-111-1-1-11-1-1-1111-1-1111-11-11-1-11-11
χ11111111111111-1-1-11-11111-1-1-1-1-1-11111-1-1-111111-1-1-1-1-1-1111-1111-1-1-111-1-1-11-11-11-11-11
χ12111111111111-1-1-11-11111-1-1-1-1-1-11111-1-1-111111-1-1-1-1-1-111-11-1-1-1111-1-111-11-11-111-11-1
χ13111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1111111-1-11-111-11-1-1-1-111-11-111-11-1-11
χ14111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1111111-1-1-11-1-11-11111-1-1-11-111-1-111-1
χ15111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1111-111-11-1-1-1-1111-11-1-11-111-1
χ16111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-111-11-1-11-11111-1-11-11-1-111-1-11
χ17222222-2-2222222-2-2-2000022-2-2-2-222-2-2200-20000000000000000000000002-2-22000000
χ18222222-2-2222222-2-2-2000022-2-2-2-222-2-2200-2000000000000000000000000-222-2000000
χ19222222-2-22222-2-22-220000-2-2222222-2-2-200-200000000000000000000000022-2-2000000
χ20222222-2-22222-2-22-220000-2-2222222-2-2-200-2000000000000000000000000-2-222000000
χ2122222-222-22222-22-2-20000-2-2-2-222-2-222200-20000000022-2-20000000000000000-220000
χ2222222-222-22222-22-2-20000-2-2-2-222-2-222200-200000000-2-22200000000000000002-20000
χ2322222-222-2222-22-2-2200002222-2-2-2-222-200-20000000022220000000000000000-2-20000
χ2422222-222-2222-22-2-2200002222-2-2-2-222-200-200000000-2-2-2-20000000000000000220000
χ2522222-2-2-2-22222-2-2222i2i−2i−2i-2-222-2-2-2-2-2-222i−2i22i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ2622222-2-2-2-22222-2-222−2i−2i2i2i-2-222-2-2-2-2-2-22−2i2i2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ2722222-2-2-2-2222-2222-22i2i−2i−2i22-2-222-2-2-2-2-2−2i2i22i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ2822222-2-2-2-2222-2222-2−2i−2i2i2i22-2-222-2-2-2-2-22i−2i2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ292222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1000022-1-122-1-1-1-1-1-10000000000
χ302222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-10000-2-211-2-21111110000000000
χ312222-12222-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-2-2-111111111000022-1-1-2-2-1-111110000000000
χ322222-12222-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-2-2-1111111110000-2-2112211-1-1-1-10000000000
χ332222-12222-1-1-1-2-2-22-22222111111-1-1-1-11-2-2-1-1-1-1-1111100002-2-1-12-211-1-1110000000000
χ342222-12222-1-1-1-2-2-22-22222111111-1-1-1-11-2-2-1-1-1-1-111110000-2211-22-1-111-1-10000000000
χ352222-12222-1-1-1-2-2-22-2-2-2-2-2111111-1-1-1-1122-11111-1-1-1-100002-2-1-1-221111-1-10000000000
χ362222-12222-1-1-1-2-2-22-2-2-2-2-2111111-1-1-1-1122-11111-1-1-1-10000-22112-2-1-1-1-1110000000000
χ372222-1-2-2-2-2-1-1-12-2-2222i2i−2i−2i11-1-1111111-12i−2i-1−i−iii−i−iii000000−i3i300−i3i33−33−30000000000
χ382222-1-2-2-2-2-1-1-12-2-2222i2i−2i−2i11-1-1111111-12i−2i-1−i−iii−i−iii000000i3−i300i3−i3−33−330000000000
χ392222-1-2-2-2-2-1-1-12-2-222−2i−2i2i2i11-1-1111111-1−2i2i-1ii−i−iii−i−i000000−i3i300−i3i3−33−330000000000
χ402222-1-2-2-2-2-1-1-12-2-222−2i−2i2i2i11-1-1111111-1−2i2i-1ii−i−iii−i−i000000i3−i300i3−i33−33−30000000000
χ412222-1-2-2-2-2-1-1-1-2222-22i2i−2i−2i-1-111-1-111111−2i2i-1−i−iiiii−i−i000000−i3i300i3−i33−3−330000000000
χ422222-1-2-2-2-2-1-1-1-2222-22i2i−2i−2i-1-111-1-111111−2i2i-1−i−iiiii−i−i000000i3−i300−i3i3−333−30000000000
χ432222-1-2-2-2-2-1-1-1-2222-2−2i−2i2i2i-1-111-1-1111112i−2i-1ii−i−i−i−iii000000−i3i300i3−i3−333−30000000000
χ442222-1-2-2-2-2-1-1-1-2222-2−2i−2i2i2i-1-111-1-1111112i−2i-1ii−i−i−i−iii000000i3−i300−i3i33−3−330000000000
χ454444-24-4-44-2-2-244-4-4-40000-2-22222-2-222-20020000000000000000000000000000000000
χ464444-24-4-44-2-2-2-4-44-44000022-2-2-2-2-2-22220020000000000000000000000000000000000
χ474444-2-444-4-2-2-24-44-4-400002222-2-222-2-2-20020000000000000000000000000000000000
χ484444-2-444-4-2-2-2-44-4-440000-2-2-2-22222-2-220020000000000000000000000000000000000
χ4944-4-44400-44-4-40000022−2222−220000004-400000022−2222−22000000000000000000000000000000
χ5044-4-44400-44-4-400000−2222−22220000004-4000000−2222−2222000000000000000000000000000000
χ5144-4-44-40044-4-400000−2i22i22i2−2i2000000-44000000−2i22i22i2−2i2000000000000000000000000000000
χ5244-4-44-40044-4-4000002i2−2i2−2i22i2000000-440000002i2−2i2−2i22i2000000000000000000000000000000
χ5344-4-4-2400-4-2220000022−2222−220023−2323−23-22000000−22−226−66−600000000000000000000000000
χ5444-4-4-2400-4-2220000022−2222−2200−2323−2323-22000000−22−22−66−6600000000000000000000000000
χ5544-4-4-2400-4-22200000−2222−22220023−2323−23-220000002−22−2−66−6600000000000000000000000000
χ5644-4-4-2400-4-22200000−2222−222200−2323−2323-220000002−22−26−66−600000000000000000000000000
χ5744-4-4-2-4004-22200000−2i22i22i2−2i20023−23−23232-2000000i2−i2−i2i2−i6i6i6−i600000000000000000000000000
χ5844-4-4-2-4004-22200000−2i22i22i2−2i200−232323−232-2000000i2−i2−i2i2i6−i6−i6i600000000000000000000000000
χ5944-4-4-2-4004-222000002i2−2i2−2i22i20023−23−23232-2000000−i2i2i2−i2i6−i6−i6i600000000000000000000000000
χ6044-4-4-2-4004-222000002i2−2i2−2i22i200−232323−232-2000000−i2i2i2−i2−i6i6i6−i600000000000000000000000000
χ614-44-4404-40-4-44000000000000000004-4000000000000004i−4i0000000000000000000000
χ624-44-4404-40-4-44000000000000000004-400000000000000−4i4i0000000000000000000000
χ634-44-440-440-4-4400000000000000000-440000000000004i−4i000000000000000000000000
χ644-44-440-440-4-4400000000000000000-44000000000000−4i4i000000000000000000000000
χ658-88-8-408-8044-400000000000000000-4400000000000000000000000000000000000000
χ668-88-8-40-88044-4000000000000000004-400000000000000000000000000000000000000
χ678-8-8880000-88-8000000000000000000000000000000000000000000000000000000000
χ688-8-88-400004-4400000000043−430000000000000000000000000000000000000000000000
χ698-8-88-400004-44000000000−43430000000000000000000000000000000000000000000000

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