Finite Group Databasebeta

← Group #10694679

Character table — Group #10694679

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444444466666664488888888121212121212121212121212242424242424242424242424242424242244666612121212888888888888
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
χ91111-1-1111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ101111-1-1111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−ii−ii
χ111111-1-1111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−ii−ii
χ121111-1-1111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiii−ii−i
χ131111-1-1111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111ii−i−i−i−iiii−i−ii
χ141111-1-1111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111−i−iiiii−i−i−iii−i
χ151111-1-1111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1ii−i−i−i−iii−iii−i
χ161111-1-1111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ17222222222-2-2-2-2222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ192222222-2-222-2-2-2-222222222-20000000022-2-222-2-2-2-2-2-2000000000000000000000000000000002i−2i2i−2i0000
χ202222222-2-222-2-2-2-222222222-20000000022-2-222-2-2-2-2-2-200000000000000000000000000000000−2i2i−2i2i0000
χ212222222-2-2-2-222-2-22222222-2200000000-2-222-2-222-2-2-2-200000000000000000000000000002i−2i2i−2i00000000
χ222222222-2-2-2-222-2-22222222-2200000000-2-222-2-222-2-2-2-20000000000000000000000000000−2i2i−2i2i00000000
χ23222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ24222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ25222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ26222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ27222222-122-2-2-2-222-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-122-2-2-2-222-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222-2-22211111111-1-1-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ30222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222-2-22211111111-1-1-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ312222-2-22222222-2-2-2-2-2-2222-2-222-2-2-2-222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ322222-2-22222222-2-2-2-2-2-2222-2-2-2-22222-2-2-2-2-2-22222-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ332222-2-22-2-222-2-222-2-2-2-2222-2200000000-2-22222-2-222-2-200000000000000000000000000002-2-2200000000
χ342222-2-22-2-222-2-222-2-2-2-2222-2200000000-2-22222-2-222-2-20000000000000000000000000000-222-200000000
χ352222-2-22-2-2-2-22222-2-2-2-22222-20000000022-2-2-2-22222-2-2000000000000000000000000000000002-2-220000
χ362222-2-22-2-2-2-22222-2-2-2-22222-20000000022-2-2-2-22222-2-200000000000000000000000000000000-222-20000
χ372222-2-2-1222222-2-21111-1-1-1-2-222-2-2-2-2221111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ382222-2-2-1222222-2-21111-1-1-1-2-222-2-2-2-2221111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ392222-2-2-1222222-2-21111-1-1-1-2-2-2-22222-2-21111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i3000000000000
χ402222-2-2-1222222-2-21111-1-1-1-2-2-2-22222-2-21111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i3000000000000
χ412222-2-2-122-2-2-2-2-2-21111-1-1-1222222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-111000000000000
χ422222-2-2-122-2-2-2-2-2-21111-1-1-1222222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-1000000000000
χ432222-2-2-122-2-2-2-2-2-21111-1-1-122-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-12-2-22-1-11111-1-1000000000000
χ442222-2-2-122-2-2-2-2-2-21111-1-1-122-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-222-211-1-1-1-111000000000000
χ45444444-2-4-444-4-4-4-4-2-2-2-2-2-2-24-400000000-2-222-2-22222220000000000000000000000000000000000000000
χ46444444-2-4-4-4-444-4-4-2-2-2-2-2-2-2-440000000022-2-222-2-222220000000000000000000000000000000000000000
χ474444-4-4-2-4-444-4-4442222-2-2-2-440000000022-2-2-2-222-2-2220000000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-444442222-2-2-24-400000000-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ4944-4-400400004-40000004-4-40000−2i22i2−2i22i2000000004-400000000−2i2−2i22i22i2−2i2−2i22i22i20000000000000000000000000000
χ5044-4-400400004-40000004-4-400002i2−2i22i2−2i2000000004-4000000002i22i2−2i2−2i22i22i2−2i2−2i20000000000000000000000000000
χ5144-4-40040000-440000004-4-40000−2i22i22i2−2i200000000-4400000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000
χ5244-4-40040000-440000004-4-400002i2−2i2−2i22i200000000-44000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000
χ5344-4-400-200004-400−2i3−2i32i32i3-2220000−2i22i2−2i22i20000−2i32i300-22000066−6−6i2i2−i2−i2i2i2−i2−i266−6−6000000000000000000000000
χ5444-4-400-200004-400−2i3−2i32i32i3-22200002i2−2i22i2−2i20000−2i32i300-220000−6−666−i2−i2i2i2−i2−i2i2i2−6−666000000000000000000000000
χ5544-4-400-200004-4002i32i3−2i3−2i3-2220000−2i22i2−2i22i200002i3−2i300-220000−6−666i2i2−i2−i2i2i2−i2−i2−6−666000000000000000000000000
χ5644-4-400-200004-4002i32i3−2i3−2i3-22200002i2−2i22i2−2i200002i3−2i300-22000066−6−6−i2−i2i2i2−i2−i2i2i266−6−6000000000000000000000000
χ5744-4-400-20000-4400−2i3−2i32i32i3-2220000−2i22i22i2−2i200002i3−2i3002-20000−6−666i2i2−i2−i2−i2−i2i2i266−6−6000000000000000000000000
χ5844-4-400-20000-4400−2i3−2i32i32i3-22200002i2−2i2−2i22i200002i3−2i3002-2000066−6−6−i2−i2i2i2i2i2−i2−i2−6−666000000000000000000000000
χ5944-4-400-20000-44002i32i3−2i3−2i3-2220000−2i22i22i2−2i20000−2i32i3002-2000066−6−6i2i2−i2−i2−i2−i2i2i2−6−666000000000000000000000000
χ6044-4-400-20000-44002i32i3−2i3−2i3-22200002i2−2i2−2i22i20000−2i32i3002-20000−6−666−i2−i2i2i2i2i2−i2−i266−6−6000000000000000000000000
χ614-44-4004004-400000000-44-400−2i22i20000−2i22i200004-4000000−2i22i2−2i22i200000000−2i22i2−2i22i2000000000000000000000000
χ624-44-4004004-400000000-44-4002i2−2i200002i2−2i200004-40000002i2−2i22i2−2i2000000002i2−2i22i2−2i2000000000000000000000000
χ634-44-400400-4400000000-44-400−2i22i200002i2−2i20000-44000000−2i22i2−2i22i2000000002i2−2i22i2−2i2000000000000000000000000
χ644-44-400400-4400000000-44-4002i2−2i20000−2i22i20000-440000002i2−2i22i2−2i200000000−2i22i2−2i22i2000000000000000000000000
χ654-44-400-2004-40000−2i32i3−2i32i32-2200−2i22i20000−2i22i2−2i32i300-22000000i2−i2i2−i26−66−66−66−6i2−i2i2−i2000000000000000000000000
χ664-44-400-2004-40000−2i32i3−2i32i32-22002i2−2i200002i2−2i2−2i32i300-22000000−i2i2−i2i2−66−66−66−66−i2i2−i2i2000000000000000000000000
χ674-44-400-2004-400002i3−2i32i3−2i32-2200−2i22i20000−2i22i22i3−2i300-22000000i2−i2i2−i2−66−66−66−66i2−i2i2−i2000000000000000000000000
χ684-44-400-2004-400002i3−2i32i3−2i32-22002i2−2i200002i2−2i22i3−2i300-22000000−i2i2−i2i26−66−66−66−6−i2i2−i2i2000000000000000000000000
χ694-44-400-200-440000−2i32i3−2i32i32-2200−2i22i200002i2−2i22i3−2i3002-2000000i2−i2i2−i2−66−666−66−6−i2i2−i2i2000000000000000000000000
χ704-44-400-200-440000−2i32i3−2i32i32-22002i2−2i20000−2i22i22i3−2i3002-2000000−i2i2−i2i26−66−6−66−66i2−i2i2−i2000000000000000000000000
χ714-44-400-200-4400002i3−2i32i3−2i32-2200−2i22i200002i2−2i2−2i32i3002-2000000i2−i2i2−i26−66−6−66−66−i2i2−i2i2000000000000000000000000
χ724-44-400-200-4400002i3−2i32i3−2i32-22002i2−2i20000−2i22i2−2i32i3002-2000000−i2i2−i2i2−66−666−66−6i2−i2i2−i2000000000000000000000000
χ734-4-444-444-400004-44-4-44-4-440000000000000000004-44-40000000000000000000000000000000000000000
χ744-4-444-44-440000-444-4-44-4-44000000000000000000-44-440000000000000000000000000000000000000000
χ754-4-444-4-24-400004-4-222-222-2000000000000000000-22-22−2i32i32i3−2i30000−2i32i32i3−2i30000000000000000000000000000
χ764-4-444-4-24-400004-4-222-222-2000000000000000000-22-222i3−2i3−2i32i300002i3−2i3−2i32i30000000000000000000000000000
χ774-4-444-4-2-440000-44-222-222-20000000000000000002-22-20000−2i32i32i3−2i30000−2i32i32i3−2i3000000000000000000000000
χ784-4-444-4-2-440000-44-222-222-20000000000000000002-22-200002i3−2i3−2i32i300002i3−2i3−2i32i3000000000000000000000000
χ794-4-44-4444-40000-44-444-4-4-44000000000000000000-444-40000000000000000000000000000000000000000
χ804-4-44-444-4400004-4-444-4-4-440000000000000000004-4-440000000000000000000000000000000000000000
χ814-4-44-44-24-40000-442-2-2222-20000000000000000002-2-22−2i32i32i3−2i300002i3−2i3−2i32i30000000000000000000000000000
χ824-4-44-44-24-40000-442-2-2222-20000000000000000002-2-222i3−2i3−2i32i30000−2i32i32i3−2i30000000000000000000000000000
χ834-4-44-44-2-4400004-42-2-2222-2000000000000000000-222-20000−2i32i32i3−2i300002i3−2i3−2i32i3000000000000000000000000
χ844-4-44-44-2-4400004-42-2-2222-2000000000000000000-222-200002i3−2i3−2i32i30000−2i32i32i3−2i3000000000000000000000000

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