Finite Group Databasebeta

← Group #10694828

Character table — Group #10694828

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122222344444444666666644888888881212121212121212121212122424242424242424242424242424242444441212121212121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9111111111-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ10111111111-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−ii−ii
χ11111111111-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−ii−ii
χ12111111111-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiii−ii−i
χ13111111111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111ii−i−i−i−iiii−i−ii
χ14111111111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111−i−iiiii−i−i−iii−i
χ15111111111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1ii−i−i−i−iii−iii−i
χ16111111111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ172222222-2-222-2-2222222222-2-2000000002222-2-2-2-2-2-2-2-2000000000000000000000000000000002-22-20000
χ182222222-2-222-2-2222222222-2-2000000002222-2-2-2-2-2-2-2-200000000000000000000000000000000-22-220000
χ192222222-2-2-2-222-2-22222222-2200000000-2-2-2-2-2-22222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ202222222-2-2-2-222-2-22222222-2200000000-2-2-2-2-2-22222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ21222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ23222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ24222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ25222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-22222-2-2-2-21111-1-11111-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-111000000000000
χ26222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-22222-2-2-2-21111-1-11111-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-1000000000000
χ27222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-2-2-2-2-222221111-1-11111-1-111111111-1-1-1-1-1-1-1-12-2-22-1-11111-1-1000000000000
χ28222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-2-2-2-2-222221111-1-11111-1-111111111-1-1-1-1-1-1-1-1-222-211-1-1-1-111000000000000
χ292222-2-22222222-2-2-2-2-2-2222-2-222-2-222-2-222-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ302222-2-22222222-2-2-2-2-2-2222-2-2-2-222-2-22222-2-2-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ312222-2-2222-2-2-2-222-2-2-2-2222-2222-2-2-2-222-2-222-2-2-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ322222-2-2222-2-2-2-222-2-2-2-2222-22-2-22222-2-2-2-222-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ332222-2-22-2-222-2-2-2-2-2-2-2-2222220000000022-2-222-2-222-2-200000000000000000000000000002i−2i2i−2i00000000
χ342222-2-22-2-222-2-2-2-2-2-2-2-2222220000000022-2-222-2-222-2-20000000000000000000000000000−2i2i−2i2i00000000
χ352222-2-22-2-2-2-22222-2-2-2-22222-200000000-2-2222222-2-2-2-200000000000000000000000000002-2-2200000000
χ362222-2-22-2-2-2-22222-2-2-2-22222-200000000-2-2222222-2-2-2-20000000000000000000000000000-222-200000000
χ372222-2-2-1222222-2-21111-1-1-1-2-222-2-222-2-2-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ382222-2-2-1222222-2-21111-1-1-1-2-222-2-222-2-2-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ392222-2-2-1222222-2-21111-1-1-1-2-2-2-222-2-222-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ402222-2-2-1222222-2-21111-1-1-1-2-2-2-222-2-222-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ412222-2-2-122-2-2-2-2221111-1-1-1-2222-2-2-2-22211-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ422222-2-2-122-2-2-2-2221111-1-1-1-2222-2-2-2-22211-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ432222-2-2-122-2-2-2-2221111-1-1-1-22-2-22222-2-211-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i3000000000000
χ442222-2-2-122-2-2-2-2221111-1-1-1-22-2-22222-2-211-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i3000000000000
χ45444444-2-4-444-4-444-2-2-2-2-2-2-2-4-400000000-2-2-2-2222222220000000000000000000000000000000000000000
χ46444444-2-4-4-4-444-4-4-2-2-2-2-2-2-2-4400000000222222-2-2-2-2220000000000000000000000000000000000000000
χ474444-4-4-2-4-444-4-4-4-42222-2-2-24400000000-2-222-2-222-2-2220000000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-444442222-2-2-24-40000000022-2-2-2-2-2-222220000000000000000000000000000000000000000
χ4944-4-44-44004-4004-444-4-44-4-400000000004-44-4000000000000000000000000000000000000000000000000
χ5044-4-44-4400-4400-4444-4-44-4-40000000000-44-44000000000000000000000000000000000000000000000000
χ5144-4-44-4-2004-4004-4-2-222-2220000000000-22-2200000000i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6000000000000000000000000
χ5244-4-44-4-2004-4004-4-2-222-2220000000000-22-2200000000−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6000000000000000000000000
χ5344-4-44-4-200-4400-44-2-222-22200000000002-22-200000000i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6000000000000000000000000
χ5444-4-44-4-200-4400-44-2-222-22200000000002-22-200000000−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6000000000000000000000000
χ5544-4-4-444004-400-44-4-4444-4-400000000004-4-44000000000000000000000000000000000000000000000000
χ5644-4-4-44400-44004-4-4-4444-4-40000000000-444-4000000000000000000000000000000000000000000000000
χ5744-4-4-44-2004-400-4422-2-2-2220000000000-222-200000000i6i6−i6−i6−i6−i6i6i6i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ5844-4-4-44-2004-400-4422-2-2-2220000000000-222-200000000−i6−i6i6i6i6i6−i6−i6−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ5944-4-4-44-200-44004-422-2-2-22200000000002-2-2200000000i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ6044-4-4-44-200-44004-422-2-2-22200000000002-2-2200000000−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ614-44-400400004-4000000-44-40000−2i22i200−2i22i20000004-400000000−2i22i2−2i22i20000−2i22i2−2i22i2000000000000000000000000
χ624-44-400400004-4000000-44-400002i2−2i2002i2−2i20000004-4000000002i2−2i22i2−2i200002i2−2i22i2−2i2000000000000000000000000
χ634-44-40040000-44000000-44-40000−2i22i2002i2−2i2000000-4400000000−2i22i2−2i22i200002i2−2i22i2−2i2000000000000000000000000
χ644-44-40040000-44000000-44-400002i2−2i200−2i22i2000000-44000000002i2−2i22i2−2i20000−2i22i2−2i22i2000000000000000000000000
χ654-44-400-200004-400−2i32i3−2i32i32-220000−2i22i200−2i22i2000000-22−2i32i3006−66−6i2−i2i2−i26−66−6i2−i2i2−i2000000000000000000000000
χ664-44-400-200004-400−2i32i3−2i32i32-2200002i2−2i2002i2−2i2000000-22−2i32i300−66−66−i2i2−i2i2−66−66−i2i2−i2i2000000000000000000000000
χ674-44-400-200004-4002i3−2i32i3−2i32-220000−2i22i200−2i22i2000000-222i3−2i300−66−66i2−i2i2−i2−66−66i2−i2i2−i2000000000000000000000000
χ684-44-400-200004-4002i3−2i32i3−2i32-2200002i2−2i2002i2−2i2000000-222i3−2i3006−66−6−i2i2−i2i26−66−6−i2i2−i2i2000000000000000000000000
χ694-44-400-20000-4400−2i32i3−2i32i32-220000−2i22i2002i2−2i20000002-22i3−2i3006−66−6i2−i2i2−i2−66−66−i2i2−i2i2000000000000000000000000
χ704-44-400-20000-4400−2i32i3−2i32i32-2200002i2−2i200−2i22i20000002-22i3−2i300−66−66−i2i2−i2i26−66−6i2−i2i2−i2000000000000000000000000
χ714-44-400-20000-44002i3−2i32i3−2i32-220000−2i22i2002i2−2i20000002-2−2i32i300−66−66i2−i2i2−i26−66−6−i2i2−i2i2000000000000000000000000
χ724-44-400-20000-44002i3−2i32i3−2i32-2200002i2−2i200−2i22i20000002-2−2i32i3006−66−6−i2i2−i2i2−66−66i2−i2i2−i2000000000000000000000000
χ734-4-440044-40000000000-4-440000004i−4i0000000000004-4000000004i−4i−4i4i0000000000000000000000000000
χ744-4-440044-40000000000-4-44000000−4i4i0000000000004-400000000−4i4i4i−4i0000000000000000000000000000
χ754-4-44004-440000000000-4-44004i−4i0000000000000000-444i−4i−4i4i000000000000000000000000000000000000
χ764-4-44004-440000000000-4-4400−4i4i0000000000000000-44−4i4i4i−4i000000000000000000000000000000000000
χ774-4-4400-24-4000000−2i32i32i3−2i322-20000004i−4i000000−2i32i30000-2200000000−2i2i2i−2i−232323−23000000000000000000000000
χ784-4-4400-24-4000000−2i32i32i3−2i322-2000000−4i4i000000−2i32i30000-22000000002i−2i−2i2i23−23−2323000000000000000000000000
χ794-4-4400-24-40000002i3−2i3−2i32i322-20000004i−4i0000002i3−2i30000-2200000000−2i2i2i−2i23−23−2323000000000000000000000000
χ804-4-4400-24-40000002i3−2i3−2i32i322-2000000−4i4i0000002i3−2i30000-22000000002i−2i−2i2i−232323−23000000000000000000000000
χ814-4-4400-2-44000000−2i32i32i3−2i322-2004i−4i00000000002i3−2i300002-2−2i2i2i−2i−232323−2300000000000000000000000000000000
χ824-4-4400-2-44000000−2i32i32i3−2i322-200−4i4i00000000002i3−2i300002-22i−2i−2i2i23−23−232300000000000000000000000000000000
χ834-4-4400-2-440000002i3−2i3−2i32i322-2004i−4i0000000000−2i32i300002-2−2i2i2i−2i23−23−232300000000000000000000000000000000
χ844-4-4400-2-440000002i3−2i3−2i32i322-200−4i4i0000000000−2i32i300002-22i−2i−2i2i−232323−2300000000000000000000000000000000

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