Finite Group Databasebeta

← Group #10844985

Character table — Group #10844985

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222234444446666666444888812121212121212124444881212121212121212121224242424242424248888226666444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ511111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111
χ811111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ91111111-1-111111111111-1-1-111-1-1-1-1-1-1111111-1-11-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-11-11-1-1-1-1-1111-1
χ101111111-1-111111111111-1-1-111-1-1-1-1-1-1111111-1-11-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-1-11-111111-1-1-11
χ111111111-1-111111111111-1-1-111-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-111111111-1-1-1-11111-11-1-1111-11-111-1-1-1-1-11
χ121111111-1-111111111111-1-1-111-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-11-11-1-111111-1
χ131111111-1-111111111111-1-1-1-1-111-1-1-1-1111111-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-11-1-111-11-11-1-1-1-111-11
χ141111111-1-111111111111-1-1-1-1-111-1-1-1-1111111-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1111-11-11111-1-11-1
χ151111111-1-111111111111-1-1-1-1-111-1-1-1-11111-1-111-11-1-1-1-1-1-11111-1-1-1-1111111111-111-1-1-11-1111-1-1-1-11-1
χ161111111-1-111111111111-1-1-1-1-111-1-1-1-11111-1-111-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11-11-1-1-11111-11
χ17222222222-2-2-2-222222222-2-200002222-2-2-2-2000000-2-200000000000000002i2i−2i−2i0000000000002i−2i0000
χ18222222222-2-2-2-222222222-2-200002222-2-2-2-2000000-2-20000000000000000−2i−2i2i2i000000000000−2i2i0000
χ192222222-2-2-2-2-2-22222222-2220000-2-2-2-2-2-2-2-20000002200000000000000002i2i−2i−2i000000000000−2i2i0000
χ202222222-2-2-2-2-2-22222222-2220000-2-2-2-2-2-2-2-2000000220000000000000000−2i−2i2i2i0000000000002i−2i0000
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
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ25222222-1-2-22222-1-1-1-1-1-1-1-2-2-222-2-21111-1-1-1-122-2-22-211-1-1-1-11111-1-1-1-1111100002-2-1-111000000000000
χ26222222-1-2-22222-1-1-1-1-1-1-1-2-2-222-2-21111-1-1-1-1-2-2222-2111111-1-1-1-1-1-1-1-111110000-2211-1-1000000000000
χ27222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2221111-1-1-1-122-2-2-2211-1-1-1-111111111-1-1-1-10000-2211-1-1000000000000
χ28222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2221111-1-1-1-1-2-222-22111111-1-1-1-11111-1-1-1-100002-2-1-111000000000000
χ292222-2-22222-22-2-2-2-2-2222-22-2222222-2-22-2-220000-2-22-20000000022-2-222-2-20000000000000000000000
χ302222-2-22222-22-2-2-2-2-2222-22-2-2-2-2-222-2-22-2-220000222-200000000-2-222-2-2220000000000000000000000
χ312222-2-2222-22-22-2-2-2-2222-2-22000022-2-2-222-2000000-220000000000000000000000000022-2-200000000
χ322222-2-2222-22-22-2-2-2-2222-2-22000022-2-2-222-2000000-2200000000000000000000000000-2-22200000000
χ332222-2-22-2-22-22-2-2-2-2-22222-2222-2-2-2-2222-2-220000-22-220000000022-2-2-2-2220000000000000000000000
χ342222-2-22-2-22-22-2-2-2-2-22222-22-2-222-2-2222-2-2200002-2-2200000000-2-22222-2-20000000000000000000000
χ352222-2-22-2-2-22-22-2-2-2-222222-20000-2-222-222-20000002-2000000000000000000000000002-2-2200000000
χ362222-2-22-2-2-22-22-2-2-2-222222-20000-2-222-222-20000002-200000000000000000000000000-222-200000000
χ372222-2-2-1222-22-21111-1-1-1-22-22222-1-111-111-10000-2-2-11−i3−i3i3i3−i3−i3i3i3-1-111-1-111000000−i3i3−i3i3000000000000
χ382222-2-2-1222-22-21111-1-1-1-22-22222-1-111-111-10000-2-2-11i3i3−i3−i3i3i3−i3−i3-1-111-1-111000000i3−i3i3−i3000000000000
χ392222-2-2-1222-22-21111-1-1-1-22-2-2-2-2-2-1-111-111-1000022-11−i3−i3i3i3−i3−i3i3i311-1-111-1-1000000i3−i3i3−i3000000000000
χ402222-2-2-1222-22-21111-1-1-1-22-2-2-2-2-2-1-111-111-1000022-11i3i3−i3−i3i3i3−i3−i311-1-111-1-1000000−i3i3−i3i3000000000000
χ412222-2-2-1-2-22-22-21111-1-1-12-2222-2-211-1-1-111-10000-221-1−i3−i3i3i3i3i3−i3−i3-1-11111-1-1000000−i3i3i3−i3000000000000
χ422222-2-2-1-2-22-22-21111-1-1-12-2222-2-211-1-1-111-10000-221-1i3i3−i3−i3−i3−i3i3i3-1-11111-1-1000000i3−i3−i3i3000000000000
χ432222-2-2-1-2-22-22-21111-1-1-12-22-2-22211-1-1-111-100002-21-1−i3−i3i3i3i3i3−i3−i311-1-1-1-111000000i3−i3−i3i3000000000000
χ442222-2-2-1-2-22-22-21111-1-1-12-22-2-22211-1-1-111-100002-21-1i3i3−i3−i3−i3−i3i3i311-1-1-1-111000000−i3i3i3−i3000000000000
χ4522-2-22-22002-2-2222-2-2-22-20000000000022-2-2002i−2i000000002i−2i2i−2i000000002-22-200000000002i−2i000000
χ4622-2-22-22002-2-2222-2-2-22-20000000000022-2-2002i−2i000000002i−2i2i−2i00000000-22-220000000000−2i2i000000
χ4722-2-22-22002-2-2222-2-2-22-20000000000022-2-200−2i2i00000000−2i2i−2i2i000000002-22-20000000000−2i2i000000
χ4822-2-22-22002-2-2222-2-2-22-20000000000022-2-200−2i2i00000000−2i2i−2i2i00000000-22-2200000000002i−2i000000
χ4922-2-22-2200-222-222-2-2-22-200000000000-2-2222-20000002-22-20000000000002i−2i−2i2i000000000000002i−2i00
χ5022-2-22-2200-222-222-2-2-22-200000000000-2-2222-20000002-22-2000000000000−2i2i2i−2i00000000000000−2i2i00
χ5122-2-22-2200-222-222-2-2-22-200000000000-2-222-22000000-22-220000000000002i−2i−2i2i00000000000000−2i2i00
χ5222-2-22-2200-222-222-2-2-22-200000000000-2-222-22000000-22-22000000000000−2i2i2i−2i000000000000002i−2i00
χ53444444-244-4-4-4-4-2-2-2-2-2-2-24-4-40000-2-2-2-222220000002200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2-444000022222222000000-2-200000000000000000000000000000000000000
χ554444-4-4-244-44-442222-2-2-2-4-440000-2-2222-2-220000002-200000000000000000000000000000000000000
χ564444-4-4-2-4-4-44-442222-2-2-244-4000022-2-22-2-22000000-2200000000000000000000000000000000000000
χ5744-4-44-4-2004-4-44-2-2222-2200000000000-2-222004i−4i00000000−2i2i−2i2i000000000000000000000000000000
χ5844-4-44-4-2004-4-44-2-2222-2200000000000-2-22200−4i4i000000002i−2i2i−2i000000000000000000000000000000
χ5944-4-44-4-200-444-4-2-2222-220000000000022-2-24-4000000-22-220000000000000000000000000000000000
χ6044-4-44-4-200-444-4-2-2222-220000000000022-2-2-440000002-22-20000000000000000000000000000000000
χ6144-4-4-4440044-4-4-4-444-44-4000000000004-44-40000000000000000000000000000000000000000000000
χ6244-4-4-44400-4-444-4-444-44-400000000000-44-440000000000000000000000000000000000000000000000
χ6344-4-4-44-20044-4-422-2-22-2200000000000-22-2200000000000023−23−2323000000000000000000000000000000
χ6444-4-4-44-20044-4-422-2-22-2200000000000-22-22000000000000−232323−23000000000000000000000000000000
χ6544-4-4-44-200-4-44422-2-22-22000000000002-22-200000000−2i32i32i3−2i30000000000000000000000000000000000
χ6644-4-4-44-200-4-44422-2-22-22000000000002-22-2000000002i3−2i3−2i32i30000000000000000000000000000000000
χ674-44-40044-4000000004-4-4000−2i22i2−2i22i24-40000000000000000000000−2i22i200−2i22i2000000000000000000000000
χ684-44-40044-4000000004-4-40002i2−2i22i2−2i24-400000000000000000000002i2−2i2002i2−2i2000000000000000000000000
χ694-44-4004-44000000004-4-4000−2i22i22i2−2i2-440000000000000000000000−2i22i2002i2−2i2000000000000000000000000
χ704-44-4004-44000000004-4-40002i2−2i2−2i22i2-4400000000000000000000002i2−2i200−2i22i2000000000000000000000000
χ714-44-400-24-40000−2i32i3−2i32i3-222000−2i22i2−2i22i2-22−2i32i300000000000000000000i2−i26−6i2−i26−60000000000000000000000
χ724-44-400-24-40000−2i32i3−2i32i3-2220002i2−2i22i2−2i2-22−2i32i300000000000000000000−i2i2−66−i2i2−660000000000000000000000
χ734-44-400-24-400002i3−2i32i3−2i3-222000−2i22i2−2i22i2-222i3−2i300000000000000000000i2−i2−66i2−i2−660000000000000000000000
χ744-44-400-24-400002i3−2i32i3−2i3-2220002i2−2i22i2−2i2-222i3−2i300000000000000000000−i2i26−6−i2i26−60000000000000000000000
χ754-44-400-2-440000−2i32i3−2i32i3-222000−2i22i22i2−2i22-22i3−2i300000000000000000000i2−i26−6−i2i2−660000000000000000000000
χ764-44-400-2-440000−2i32i3−2i32i3-2220002i2−2i2−2i22i22-22i3−2i300000000000000000000−i2i2−66i2−i26−60000000000000000000000
χ774-44-400-2-4400002i3−2i32i3−2i3-222000−2i22i22i2−2i22-2−2i32i300000000000000000000i2−i2−66−i2i26−60000000000000000000000
χ784-44-400-2-4400002i3−2i32i3−2i3-2220002i2−2i2−2i22i22-2−2i32i300000000000000000000−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).