Finite Group Databasebeta

← Group #10713321

Character table — Group #10713321

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order1222223444444446668888121212124466888888121212121212121212122424242424242424242424242424242488882424242424242424444444441616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-11-111-1-111-11111111-1-1-1-11-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101111-1-11-111-1-111-11111111-1-1-1-11-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111111-1-11-111-1-111-11111111-1-1-1-11-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121111-1-11-111-1-111-11111111-1-1-1-11-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131111-1-11-1-1-11111-11111111-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ141111-1-11-1-1-11111-11111111-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ151111-1-11-1-1-11111-11111111-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ161111-1-11-1-1-11111-11111111-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ17222222222222222222-2-2-2-222222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222-2-2-2-2222222-2-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ192222222-22222-2-2-22220000-2-2-2-2-2-22200000022-2-222-2-2-2-2000000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ202222222-22222-2-2-22220000-2-2-2-2-2-22200000022-2-222-2-2-2-2000000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ212222222-2-2-2-2-2-2-2-22220000-2-2-2-22222000000-2-222-2-222-2-2000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ222222222-2-2-2-2-2-2-2-22220000-2-2-2-22222000000-2-222-2-222-2-2000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ23222222-122222222-1-1-12222-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ24222222-122222222-1-1-12222-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ25222222-122222222-1-1-1-2-2-2-2-1-1-1-122-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ26222222-122222222-1-1-1-2-2-2-2-1-1-1-122-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ27222222-12-2-2-2-2222-1-1-12222-1-1-1-1-2-2-1-122-2-2-2-211111111-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ28222222-12-2-2-2-2222-1-1-12222-1-1-1-1-2-2-1-122-2-2-2-211111111-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ29222222-12-2-2-2-2222-1-1-1-2-2-2-2-1-1-1-1-2-2-1-1-2-2222211111111-1-111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ30222222-12-2-2-2-2222-1-1-1-2-2-2-2-1-1-1-1-2-2-1-1-2-2222211111111-1-111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ312222-2-22222-2-2-2-2222200002222-22-2-200000022-2-2-2-222-2-2000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ322222-2-22222-2-2-2-2222200002222-22-2-200000022-2-2-2-222-2-2000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ332222-2-222-2-222-2-22222000022222-2-2-2000000-2-22222-2-2-2-2000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ342222-2-222-2-222-2-22222000022222-2-2-2000000-2-22222-2-2-2-2000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ352222-2-22-222-2-222-2222-2-2-2-2-2-2-2-22-2-2-222-2-2222222-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ362222-2-22-2-2-22222-2222-2-2-2-2-2-2-2-2-22-2-22222-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ372222-2-2-1-222-2-222-2-1-1-1222211112-211-2-222-2-2-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111112i−2i2i−2i−i−iii−i−iii0000000000000000
χ382222-2-2-1-222-2-222-2-1-1-1222211112-211-2-222-2-2-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ392222-2-2-1-222-2-222-2-1-1-1-2-2-2-211112-21122-2-222-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-100003−3−333−3−330000000000000000
χ402222-2-2-1-222-2-222-2-1-1-1-2-2-2-211112-21122-2-222-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-10000−333−3−333−30000000000000000
χ412222-2-2-1-2-2-22222-2-1-1-122221111-2211-2-2-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-12i−2i−2i2i−i−iiiii−i−i0000000000000000
χ422222-2-2-1-2-2-22222-2-1-1-122221111-2211-2-2-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−2i2i2i−2iii−i−i−i−iii0000000000000000
χ432222-2-2-1-2-2-22222-2-1-1-1-2-2-2-21111-22112222-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100003−3−33−333−30000000000000000
χ442222-2-2-1-2-2-22222-2-1-1-1-2-2-2-21111-22112222-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000−333−33−3−330000000000000000
χ4522-2-22-22200002-2-22-2-222-2-222-2-2002-22-20000000000002-222-2-222-2-20000000000000000000000002-22-200000000
χ4622-2-22-22200002-2-22-2-222-2-222-2-2002-22-20000000000002-222-2-222-2-2000000000000000000000000-22-2200000000
χ4722-2-22-22200002-2-22-2-2-2-22222-2-2002-2-220000000000002-2-2-222-2-222000000000000000000002i−2i2i−2i000000000000
χ4822-2-22-22200002-2-22-2-2-2-22222-2-2002-2-220000000000002-2-2-222-2-22200000000000000000000−2i2i−2i2i000000000000
χ4922-2-2-222-200002-222-2-222-2-2-2-22200-22-220000000000002-222-2-2-2-2220000000000000000000000002i−2i−2i2i00000000
χ5022-2-2-222-200002-222-2-222-2-2-2-22200-22-220000000000002-222-2-2-2-222000000000000000000000000−2i2i2i−2i00000000
χ5122-2-2-222-200002-222-2-2-2-222-2-22200-222-20000000000002-2-2-22222-2-2000000000000000000002-2-22000000000000
χ5222-2-2-222-200002-222-2-2-2-222-2-22200-222-20000000000002-2-2-22222-2-200000000000000000000-222-2000000000000
χ53444444-2-44444-4-4-4-2-2-200002222-4-4-2-2000000-2-222-2-2222200000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-4-4-2-2-20000222244-2-200000022-2-222-2-22200000000000000000000000000000000000000000000
χ554444-4-4-2444-4-4-4-44-2-2-20000-2-2-2-2-4422000000-2-22222-2-22200000000000000000000000000000000000000000000
χ564444-4-4-24-4-444-4-44-2-2-20000-2-2-2-24-42200000022-2-2-2-2222200000000000000000000000000000000000000000000
χ5744-4-44-44-40000-4444-4-40000-4-444004-400000000000000-4400000000000000000000000000000000000000000000
χ5844-4-44-4-2400004-4-4-22244-4-4-2-22200-224-4000000000000-22-2-222-2-222000000000000000000000000000000000000
χ5944-4-44-4-2400004-4-4-222-4-444-2-22200-22-44000000000000-2222-2-222-2-2000000000000000000000000000000000000
χ6044-4-44-4-2-40000-444-222000022-2-200-22000000000000002-200000000−2i3−2i32i32i3−2i3−2i32i32i30000000000000000000000000000
χ6144-4-44-4-2-40000-444-222000022-2-200-22000000000000002-2000000002i32i3−2i3−2i32i32i3−2i3−2i30000000000000000000000000000
χ6244-4-4-44440000-44-44-4-4000044-4-400-4400000000000000-4400000000000000000000000000000000000000000000
χ6344-4-4-44-240000-44-4-2220000-2-222002-2000000000000002-200000000−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000
χ6444-4-4-44-240000-44-4-2220000-2-222002-2000000000000002-2000000002i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000
χ6544-4-4-44-2-400004-44-22244-4-422-2-2002-2-44000000000000-22-2-22222-2-2000000000000000000000000000000000000
χ6644-4-4-44-2-400004-44-222-4-44422-2-2002-24-4000000000000-2222-2-2-2-222000000000000000000000000000000000000
χ674-44-40040004-4000-44-4−2i22i2−2i22i2000000000000−2i22i200004-40000−2i22i2−2i22i200000000−2i22i2−2i22i20000000000000000000000000000
χ684-44-40040004-4000-44-42i2−2i22i2−2i20000000000002i2−2i200004-400002i2−2i22i2−2i2000000002i2−2i22i2−2i20000000000000000000000000000
χ694-44-4004000-44000-44-4−2i22i2−2i22i20000000000002i2−2i20000-440000−2i22i2−2i22i2000000002i2−2i22i2−2i20000000000000000000000000000
χ704-44-4004000-44000-44-42i2−2i22i2−2i2000000000000−2i22i20000-4400002i2−2i22i2−2i200000000−2i22i2−2i22i20000000000000000000000000000
χ714-44-400-20004-40002-22−2i22i2−2i22i223−2323−2300000000−2i22i20023−23-220000i2−i2i2−i2i6−i6i6−i6i6−i6i6−i6i2−i2i2−i20000000000000000000000000000
χ724-44-400-20004-40002-22−2i22i2−2i22i2−2323−232300000000−2i22i200−2323-220000i2−i2i2−i2−i6i6−i6i6−i6i6−i6i6i2−i2i2−i20000000000000000000000000000
χ734-44-400-20004-40002-222i2−2i22i2−2i223−2323−23000000002i2−2i20023−23-220000−i2i2−i2i2−i6i6−i6i6−i6i6−i6i6−i2i2−i2i20000000000000000000000000000
χ744-44-400-20004-40002-222i2−2i22i2−2i2−2323−2323000000002i2−2i200−2323-220000−i2i2−i2i2i6−i6i6−i6i6−i6i6−i6−i2i2−i2i20000000000000000000000000000
χ754-44-400-2000-440002-22−2i22i2−2i22i223−2323−23000000002i2−2i200−23232-20000i2−i2i2−i2i6−i6i6−i6−i6i6−i6i6−i2i2−i2i20000000000000000000000000000
χ764-44-400-2000-440002-22−2i22i2−2i22i2−2323−2323000000002i2−2i20023−232-20000i2−i2i2−i2−i6i6−i6i6i6−i6i6−i6−i2i2−i2i20000000000000000000000000000
χ774-44-400-2000-440002-222i2−2i22i2−2i223−2323−2300000000−2i22i200−23232-20000−i2i2−i2i2−i6i6−i6i6i6−i6i6−i6i2−i2i2−i20000000000000000000000000000
χ784-44-400-2000-440002-222i2−2i22i2−2i2−2323−232300000000−2i22i20023−232-20000−i2i2−i2i2i6−i6i6−i6−i6i6−i6i6i2−i2i2−i20000000000000000000000000000
χ794-4-4400404i−4i00000-4-44−2i22i22i2−2i2000000000022−22004i−4i00000000−2i22i22i2−2i2000022−22−222200000000000000000000000000000000
χ804-4-4400404i−4i00000-4-442i2−2i2−2i22i20000000000−2222004i−4i000000002i2−2i2−2i22i20000−222222−2200000000000000000000000000000000
χ814-4-440040−4i4i00000-4-44−2i22i22i2−2i20000000000−222200−4i4i00000000−2i22i22i2−2i20000−222222−2200000000000000000000000000000000
χ824-4-440040−4i4i00000-4-442i2−2i2−2i22i2000000000022−2200−4i4i000000002i2−2i2−2i22i2000022−22−222200000000000000000000000000000000
χ834-4-4400-204i−4i0000022-2−2i22i22i2−2i223−23−232300000022−2200−2i2i0000−2i32i300i2−i2−i2i2i6−i6−i6i6−222−2−666−60000000000000000000000000000
χ844-4-4400-204i−4i0000022-2−2i22i22i2−2i2−232323−2300000022−2200−2i2i00002i3−2i300i2−i2−i2i2−i6i6i6−i6−222−26−6−660000000000000000000000000000
χ854-4-4400-204i−4i0000022-22i2−2i2−2i22i223−23−2323000000−222200−2i2i0000−2i32i300−i2i2i2−i2−i6i6i6−i62−2−226−6−660000000000000000000000000000
χ864-4-4400-204i−4i0000022-22i2−2i2−2i22i2−232323−23000000−222200−2i2i00002i3−2i300−i2i2i2−i2i6−i6−i6i62−2−22−666−60000000000000000000000000000
χ874-4-4400-20−4i4i0000022-2−2i22i22i2−2i223−23−2323000000−2222002i−2i00002i3−2i300i2−i2−i2i2i6−i6−i6i62−2−226−6−660000000000000000000000000000
χ884-4-4400-20−4i4i0000022-2−2i22i22i2−2i2−232323−23000000−2222002i−2i0000−2i32i300i2−i2−i2i2−i6i6i6−i62−2−22−666−60000000000000000000000000000
χ894-4-4400-20−4i4i0000022-22i2−2i2−2i22i223−23−232300000022−22002i−2i00002i3−2i300−i2i2i2−i2−i6i6i6−i6−222−2−666−60000000000000000000000000000
χ904-4-4400-20−4i4i0000022-22i2−2i2−2i22i2−232323−2300000022−22002i−2i0000−2i32i300−i2i2i2−i2i6−i6−i6i6−222−26−6−660000000000000000000000000000

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