Finite Group Databasebeta

← Group #10847306

Character table — Group #10847306

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222234444446666666444888812121212121212122244666688121212121212242424242424242488884412121212444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ511111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111
χ811111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ91111111-1-111111111111-1-1-111-1-1111-1-1-1-1111-1-111111-1-1-1-1-1-1-11111-1-1-1-111111-111-1-11-11-111-1-1-1-11-1
χ101111111-1-111111111111-1-1-111-1-1111-1-1-1-1111-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-1-11-11-1-11111-11
χ111111111-1-111111111111-1-1-111-1-1111-1-1-1-11-1-111-1-1-1-11-11111-1-11111-1-1-1-11111-11-1-1111-11-1-1-1-1-111-11
χ121111111-1-111111111111-1-1-111-1-1111-1-1-1-11-1-111-1-1-1-11-11111-1-11111-1-1-1-1-1-1-1-1-11-1-111-11-111111-1-11-1
χ131111111-1-111111111111-1-1-1-1-111111-1-1-1-1111-1-11111-11-1-1-1-1-1-1-1-1-1-111111111-11-1-111-11-1111-1-1-1-1-11
χ141111111-1-111111111111-1-1-1-1-111111-1-1-1-1111-1-11111-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1111-11-1-1-111111-1
χ151111111-1-111111111111-1-1-1-1-111111-1-1-1-11-1-111-1-1-1-1-111111-1-1-1-1-1-1111111111-111-1-1-11-11-1-1-1-1111-1
χ161111111-1-111111111111-1-1-1-1-111111-1-1-1-11-1-111-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11-111-1-11-11-11111-1-1-11
χ17222222222-2-2-2-222222222-2-20000-2-2-22222-200000000000000-2-2000000002i2i−2i−2i0000000000002i−2i0000
χ18222222222-2-2-2-222222222-2-20000-2-2-22222-200000000000000-2-200000000−2i−2i2i2i000000000000−2i2i0000
χ192222222-2-2-2-2-2-22222222-2220000-2-2-2-2-2-2-2-20000000000000022000000002i2i−2i−2i000000000000−2i2i0000
χ202222222-2-2-2-2-2-22222222-2220000-2-2-2-2-2-2-2-2000000000000002200000000−2i−2i2i2i0000000000002i−2i0000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-2-2-2-21111221111-1-1-1-1-1-1-1-1-1-10000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-1-1-1-1-1-1111111110000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-21111-2-21111-1-111111111000022-1-1-1-1000000000000
χ25222222-1-2-22222-1-1-1-1-1-1-1-2-2-222-2-2-1-1-11111-122-2-2-1-1-1-12-2111111-1-1-1-1111100002-2-1-111000000000000
χ26222222-1-2-22222-1-1-1-1-1-1-1-2-2-222-2-2-1-1-11111-1-2-22211112-2-1-1-1-111-1-1-1-111110000-2211-1-1000000000000
χ27222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-222-1-1-11111-122-2-2-1-1-1-1-221111111111-1-1-1-10000-2211-1-1000000000000
χ28222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-222-1-1-11111-1-2-2221111-22-1-1-1-1111111-1-1-1-100002-2-1-111000000000000
χ292222-2-22222-22-2-2-2-2-2222-22-222222-2-222-2-2200000000-2-200002-222-2-222-2-20000000000000000000000
χ302222-2-22222-22-2-2-2-2-2222-22-2-2-2-2-22-2-222-2-22000000002200002-2-2-222-2-2220000000000000000000000
χ312222-2-2222-22-22-2-2-2-2222-2-220000-22222-2-2-200000000000000-2200000000000000000022-2-200000000
χ322222-2-2222-22-22-2-2-2-2222-2-220000-22222-2-2-200000000000000-22000000000000000000-2-22200000000
χ332222-2-22-2-22-22-2-2-2-2-22222-2222-2-22-2-2-2-222200000000-220000-2222-2-2-2-2220000000000000000000000
χ342222-2-22-2-22-22-2-2-2-2-22222-22-2-2222-2-2-2-2222000000002-20000-22-2-22222-2-20000000000000000000000
χ352222-2-22-2-2-22-22-2-2-2-222222-20000-222-2-222-2000000000000002-20000000000000000002-2-2200000000
χ362222-2-22-2-2-22-22-2-2-2-222222-20000-222-2-222-2000000000000002-2000000000000000000-222-200000000
χ372222-2-2-1222-22-21111-1-1-1-22-22222-111-1-111-10000−i3−i3i3i3-2-2−i3−i3i3i3-11-1-111-1-111000000−i3i3−i3i3000000000000
χ382222-2-2-1222-22-21111-1-1-1-22-22222-111-1-111-10000i3i3−i3−i3-2-2i3i3−i3−i3-11-1-111-1-111000000i3−i3i3−i3000000000000
χ392222-2-2-1222-22-21111-1-1-1-22-2-2-2-2-2-111-1-111-10000−i3−i3i3i322−i3−i3i3i3-1111-1-111-1-1000000i3−i3i3−i3000000000000
χ402222-2-2-1222-22-21111-1-1-1-22-2-2-2-2-2-111-1-111-10000i3i3−i3−i322i3i3−i3−i3-1111-1-111-1-1000000−i3i3−i3i3000000000000
χ412222-2-2-1-2-22-22-21111-1-1-12-2222-2-2-11111-1-1-10000−i3−i3i3i3-22i3i3−i3−i31-1-1-11111-1-1000000−i3i3i3−i3000000000000
χ422222-2-2-1-2-22-22-21111-1-1-12-2222-2-2-11111-1-1-10000i3i3−i3−i3-22−i3−i3i3i31-1-1-11111-1-1000000i3−i3−i3i3000000000000
χ432222-2-2-1-2-22-22-21111-1-1-12-22-2-222-11111-1-1-10000−i3−i3i3i32-2i3i3−i3−i31-111-1-1-1-111000000i3−i3−i3i3000000000000
χ442222-2-2-1-2-22-22-21111-1-1-12-22-2-222-11111-1-1-10000i3i3−i3−i32-2−i3−i3i3i31-111-1-1-1-111000000−i3i3i3−i3000000000000
χ4522-2-22-220022-2-222-2-22-2-2000000022-20000-22-2002-22-200000000000000002-22-200000000002-2000000
χ4622-2-22-220022-2-222-2-22-2-2000000022-20000-22-2002-22-20000000000000000-22-220000000000-22000000
χ4722-2-22-220022-2-222-2-22-2-2000000022-20000-2-2200-22-2200000000000000002-22-20000000000-22000000
χ4822-2-22-220022-2-222-2-22-2-2000000022-20000-2-2200-22-220000000000000000-22-2200000000002-2000000
χ4922-2-22-2200-2-22222-2-22-2-20000000-2-2200002002i−2i0000002i−2i2i−2i00000000002i−2i−2i2i000000000000002-200
χ5022-2-22-2200-2-22222-2-22-2-20000000-2-2200002002i−2i0000002i−2i2i−2i0000000000−2i2i2i−2i00000000000000-2200
χ5122-2-22-2200-2-22222-2-22-2-20000000-2-220000200−2i2i000000−2i2i−2i2i00000000002i−2i−2i2i00000000000000-2200
χ5222-2-22-2200-2-22222-2-22-2-20000000-2-220000200−2i2i000000−2i2i−2i2i0000000000−2i2i2i−2i000000000000002-200
χ53444444-244-4-4-4-4-2-2-2-2-2-2-24-4-40000222-2-2-2-220000000000000022000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2-44400002222222200000000000000-2-2000000000000000000000000000000
χ554444-4-4-244-44-442222-2-2-2-4-4400002-2-2-2-2222000000000000002-2000000000000000000000000000000
χ564444-4-4-2-4-4-44-442222-2-2-244-400002-2-222-2-2200000000000000-22000000000000000000000000000000
χ5744-4-44-4-20044-4-4-2-222-2220000000-2-22000024-400-22-2200000000000000000000000000000000000000
χ5844-4-44-4-20044-4-4-2-222-2220000000-2-2200002-44002-22-200000000000000000000000000000000000000
χ5944-4-44-4-200-4-444-2-222-222000000022-20000-2004i−4i000000−2i2i−2i2i00000000000000000000000000000000
χ6044-4-44-4-200-4-444-2-222-222000000022-20000-200−4i4i0000002i−2i2i−2i00000000000000000000000000000000
χ6144-4-4-444004-4-44-4-4444-4-400000004-440000-40000000000000000000000000000000000000000000000
χ6244-4-4-44400-444-4-4-4444-4-40000000-44-4000040000000000000000000000000000000000000000000000
χ6344-4-4-44-2004-4-4422-2-2-2220000000-22-2000020000−2i32i32i3−2i300000000000000000000000000000000000000
χ6444-4-4-44-2004-4-4422-2-2-2220000000-22-20000200002i3−2i3−2i32i300000000000000000000000000000000000000
χ6544-4-4-44-200-444-422-2-2-22200000002-220000-2000000000023−23−232300000000000000000000000000000000
χ6644-4-4-44-200-444-422-2-2-22200000002-220000-20000000000−232323−2300000000000000000000000000000000
χ674-44-40044-400000000-44-4000−2i22i2−2i22i20004-40000000000000000000−2i22i200−2i22i2000000000000000000000000
χ684-44-40044-400000000-44-40002i2−2i22i2−2i20004-400000000000000000002i2−2i2002i2−2i2000000000000000000000000
χ694-44-4004-4400000000-44-4000−2i22i22i2−2i2000-440000000000000000000−2i22i2002i2−2i2000000000000000000000000
χ704-44-4004-4400000000-44-40002i2−2i2−2i22i2000-4400000000000000000002i2−2i200−2i22i2000000000000000000000000
χ714-44-400-24-40000−2i32i3−2i32i32-22000−2i22i2−2i22i2000-22−2i32i300000000000000000i2−i26−6i2−i26−60000000000000000000000
χ724-44-400-24-40000−2i32i3−2i32i32-220002i2−2i22i2−2i2000-22−2i32i300000000000000000−i2i2−66−i2i2−660000000000000000000000
χ734-44-400-24-400002i3−2i32i3−2i32-22000−2i22i2−2i22i2000-222i3−2i300000000000000000i2−i2−66i2−i2−660000000000000000000000
χ744-44-400-24-400002i3−2i32i3−2i32-220002i2−2i22i2−2i2000-222i3−2i300000000000000000−i2i26−6−i2i26−60000000000000000000000
χ754-44-400-2-440000−2i32i3−2i32i32-22000−2i22i22i2−2i20002-22i3−2i300000000000000000i2−i26−6−i2i2−660000000000000000000000
χ764-44-400-2-440000−2i32i3−2i32i32-220002i2−2i2−2i22i20002-22i3−2i300000000000000000−i2i2−66i2−i26−60000000000000000000000
χ774-44-400-2-4400002i3−2i32i3−2i32-22000−2i22i22i2−2i20002-2−2i32i300000000000000000i2−i2−66−i2i26−60000000000000000000000
χ784-44-400-2-4400002i3−2i32i3−2i32-220002i2−2i2−2i22i20002-2−2i32i300000000000000000−i2i26−6i2−i2−660000000000000000000000
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).