Finite Group Databasebeta

← Group #10691601

Character table — Group #10691601

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222234444446666666444444412121212121212124488881212121212121212121224242424242424248888226666888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ91111111-111-1-1-111111111-111-1-1-1-1-1-1-111111-111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−i1-111-1-1i−iii−i−iii−i−ii−i
χ101111111-111-1-1-111111111-111-1-1-1-1-1-1-111111-111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii1-111-1-1−ii−i−iii−i−iii−ii
χ111111111-111-1-1-111111111-111-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1-1-1-1-1-1-11111ii−i−i-11-1-111i−iii−i−i−i−iii−ii
χ121111111-111-1-1-111111111-111-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1-1-1-1-1-1-11111−i−iii-11-1-111−ii−i−iiiii−i−ii−i
χ131111111-111-1-1-111111111-1-1-111-1-1-1-1-11111-1111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i-11-1-111i−i−i−iiiii−i−i−ii
χ141111111-111-1-1-111111111-1-1-111-1-1-1-1-11111-1111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii-11-1-111−iiii−i−i−i−iiii−i
χ151111111-111-1-1-111111111-1-1-111-1-1-1-1-11111-11-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−i1-111-1-1i−i−i−iii−i−iiii−i
χ161111111-111-1-1-111111111-1-1-111-1-1-1-1-11111-11-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iii1-111-1-1−iiii−i−iii−i−i−ii
χ1722222222-2-22222222222-2-20000-22222-2-2-2-2000000-2-200000000000000002222000000-2-20000000000
χ1822222222-2-22222222222-2-20000-22222-2-2-2-2000000-2-20000000000000000-2-2-2-2000000220000000000
χ192222222-2-2-2-2-2-22222222-2200002-2-2-2-2-2-2-2-20000002200000000000000002i2i−2i−2i000000−2i2i0000000000
χ202222222-2-2-2-2-2-22222222-2200002-2-2-2-2-2-2-2-2000000220000000000000000−2i−2i2i2i0000002i−2i0000000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ25222222-1-222-2-2-2-1-1-1-1-1-1-12-222-2-2-21111-1-1-1-12-222-2-211-1-1-1-11111-1-1-1-1111100002-2-1-111000000000000
χ26222222-1-222-2-2-2-1-1-1-1-1-1-12-222-2-2-21111-1-1-1-12-2-2-22211-1-1-1-111111111-1-1-1-10000-2211-1-1000000000000
χ27222222-1-222-2-2-2-1-1-1-1-1-1-12-2-2-222-21111-1-1-1-1-2222-2-2111111-1-1-1-1-1-1-1-111110000-2211-1-1000000000000
χ28222222-1-222-2-2-2-1-1-1-1-1-1-12-2-2-222-21111-1-1-1-1-22-2-222111111-1-1-1-11111-1-1-1-100002-2-1-111000000000000
χ292222-2-22222-22-2-2-2-2-2222-2-222-2-2222-2-22-2-22-2200002-222-2-222-2-2000000000000000000000000000000
χ302222-2-22222-22-2-2-2-2-2222-2-2-2-222222-2-22-2-222-200002-2-2-222-2-222000000000000000000000000000000
χ312222-2-222-2-2-22-2-2-2-2-2222220000-222-2-2-222-2000000-2200000000000000000000000000002i−2i2i−2i000000
χ322222-2-222-2-2-22-2-2-2-2-2222220000-222-2-2-222-2000000-220000000000000000000000000000−2i2i−2i2i000000
χ332222-2-22-2222-22-2-2-2-2222-222222-2-2-2222-2-22-2-20000-2222-2-2-2-222000000000000000000000000000000
χ342222-2-22-2222-22-2-2-2-2222-22-2-2-2-2-2-2-2222-2-22220000-22-2-22222-2-2000000000000000000000000000000
χ352222-2-22-2-2-22-22-2-2-2-22222-200002-2-222-222-20000002-200000000000000000000000000002-2-22000000
χ362222-2-22-2-2-22-22-2-2-2-22222-200002-2-222-222-20000002-20000000000000000000000000000-222-2000000
χ372222-2-2-1222-22-21111-1-1-1-2-222-2-22-1-111-111-1-220000-11-1-111-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ382222-2-2-1222-22-21111-1-1-1-2-222-2-22-1-111-111-1-220000-11-1-111-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ392222-2-2-1222-22-21111-1-1-1-2-2-2-2222-1-111-111-12-20000-1111-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ402222-2-2-1222-22-21111-1-1-1-2-2-2-2222-1-111-111-12-20000-1111-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ412222-2-2-1-2222-221111-1-1-1-222222-211-1-1-111-1-2-200001-1-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ422222-2-2-1-2222-221111-1-1-1-222222-211-1-1-111-1-2-200001-1-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ432222-2-2-1-2222-221111-1-1-1-22-2-2-2-2-211-1-1-111-12200001-111-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ442222-2-2-1-2222-221111-1-1-1-22-2-2-2-2-211-1-1-111-12200001-111-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ4522-2-22-22200-2-2222-2-22-2-200000002-22-2000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i0000000000002−22−200
χ4622-2-22-22200-2-2222-2-22-2-200000002-22-2000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i000000000000−22−2200
χ4722-2-22-22200-2-2222-2-22-2-200000002-22-2000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i000000000000−22−2200
χ4822-2-22-22200-2-2222-2-22-2-200000002-22-2000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i0000000000002−22−200
χ4922-2-22-22-20022-222-2-22-2-20000000-22-22000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i22-2-22000000000000−i2i2i2−i200
χ5022-2-22-22-20022-222-2-22-2-20000000-22-22000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2-222-2000000000000i2−i2−i2i200
χ5122-2-22-22-20022-222-2-22-2-20000000-22-22000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i22-2-22000000000000i2−i2−i2i200
χ5222-2-22-22-20022-222-2-22-2-20000000-22-22000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2-222-2000000000000−i2i2i2−i200
χ53444444-24-4-4444-2-2-2-2-2-2-2-4-40000-4-2-2-2-222220000002200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2-440000422222222000000-2-200000000000000000000000000000000000000
χ554444-4-4-24-4-4-44-42222-2-2-2440000-4-2-2222-2-220000002-200000000000000000000000000000000000000
χ564444-4-4-2-4-4-44-442222-2-2-24-40000422-2-22-2-22000000-2200000000000000000000000000000000000000
χ5744-4-44-4-2400-4-44-2-222-2220000000-22-22000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000
χ5844-4-44-4-2400-4-44-2-222-2220000000-22-220000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000
χ5944-4-44-4-2-40044-4-2-222-22200000002-22-2000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000
χ6044-4-44-4-2-40044-4-2-222-22200000002-22-20000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000
χ6144-4-4-4444004-4-4-4-4444-4-400000004-4-4400000000000000000000000000000000000000000000000000
χ6244-4-4-444-400-444-4-4444-4-40000000-444-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-24004-4-422-2-2-2220000000-222-2000000000000000000006−6−666−6−660000000000000000000000
χ6444-4-4-44-24004-4-422-2-2-2220000000-222-200000000000000000000−666−6−666−60000000000000000000000
χ6544-4-4-44-2-400-44422-2-2-22200000002-2-22000000000000000000006−6−66−666−60000000000000000000000
χ6644-4-4-44-2-400-44422-2-2-22200000002-2-2200000000000000000000−666−66−6−660000000000000000000000
χ674-44-400404-40000000-44-400004i−4i00000400-4000000000000004i−4i000000000000000000000000000000
χ684-44-400404-40000000-44-40000−4i4i00000400-400000000000000−4i4i000000000000000000000000000000
χ694-44-40040-440000000-44-4004-40000000-4004000000004-4000000000000000000000000000000000000
χ704-44-40040-440000000-44-400-440000000-400400000000-44000000000000000000000000000000000000
χ714-44-400-204-4000−2i32i3−2i32i32-2200004i−4i00000-2−2i32i3200000000000023−23−2i2i000000000000000000000000000000
χ724-44-400-204-4000−2i32i3−2i32i32-220000−4i4i00000-2−2i32i32000000000000−23232i−2i000000000000000000000000000000
χ734-44-400-204-40002i3−2i32i3−2i32-2200004i−4i00000-22i3−2i32000000000000−2323−2i2i000000000000000000000000000000
χ744-44-400-204-40002i3−2i32i3−2i32-220000−4i4i00000-22i3−2i3200000000000023−232i−2i000000000000000000000000000000
χ754-44-400-20-44000−2i32i3−2i32i32-22004-4000000022i3−2i3-200000000-22−2i32i30000000000000000000000000000000000
χ764-44-400-20-44000−2i32i3−2i32i32-2200-44000000022i3−2i3-2000000002-22i3−2i30000000000000000000000000000000000
χ774-44-400-20-440002i3−2i32i3−2i32-22004-400000002−2i32i3-200000000-222i3−2i30000000000000000000000000000000000
χ784-44-400-20-440002i3−2i32i3−2i32-2200-4400000002−2i32i3-2000000002-2−2i32i30000000000000000000000000000000000
χ798-8-880080000000000-8-880000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-4000000−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-40000004i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000

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