Finite Group Databasebeta

← Group #10778217

Character table — Group #10778217

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order1222344444444666121212122444444661212121212122466888812121212121212122424242424242424888824661212888888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111111111111111-1-11-1-111111111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111-1-11-1-111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ911111-1-1-1-11111111-1-1-1-1-1-111111-1-111-1-111-1-1-1-111-1-11-111-1-1111111-1-1-1-111-1-11-111-1-111-1-11-111-1-1-11
χ1011111-1-1-1-11111111-1-1-1-1-1-111111-1-111-1-111-1-1-1-111-1-11-111-1-1111111-1-1-1-1-1-1111-111-1-1-1-111-11-1-1111-1
χ1111111-1-1-1-11111111-1-1-1-1-1-111111-1-111-1-111-1-1-1-1-1-1111-111-1-111-1-1-1-1111111-1-1-11-1-111-1-1111-111-1-11-1
χ1211111-1-1-1-11111111-1-1-1-1-1-111111-1-111-1-111-1-1-1-1-1-1111-111-1-111-1-1-1-11111-1-111-11-1-11111-1-1-11-1-111-11
χ1311111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111111111-1-11-1-1-111-1-11111-1-1-1-111-1-1-11-1-11111-1-11-1-1-1111-1
χ1411111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111111111-1-11-1-1-111-1-11111-1-1-1-1-1-111-11-1-111-1-111-1111-1-1-11
χ1511111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1111-1-1-111-1-1-1-1-1-1111111-1-11-111-1-1-1-1111-1-1-111-11
χ1611111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1111-1-1-111-1-1-1-1-1-11111-1-1111-111-1-111-1-1-1111-1-11-1
χ17222222222-2-2222222222-2-200-200-2-22222-2-200000000-2-20000000000000022220000000000-2-2000000
χ18222222222-2-2222222222-2-200-200-2-22222-2-200000000-2-200000000000000-2-2-2-2000000000022000000
χ192222222-2-222-2-222222222-222-2-2-222-2-2-2-2222-2220000-2-2-2-2-2-222000000000000000000000000000000
χ202222222-2-222-2-222222222-2-2-2-22222-2-2-2-222-22-2-20000-2-22222-2-2000000000000000000000000000000
χ212222222-2-2-2-2-2-22222222-2200200-2-2-2-2-2-2-2-200000000220000000000000000000000000000002i−2i2i−2i00
χ222222222-2-2-2-2-2-22222222-2200200-2-2-2-2-2-2-2-20000000022000000000000000000000000000000−2i2i−2i2i00
χ2322222-2-22222-2-2222-2-2-2-2-2222-2-2-2-2-2-2-22222-22-2-20000-22-2-22222000000000000000000000000000000
χ2422222-2-22222-2-2222-2-2-2-2-22-2-2-222-2-2-2-222222-2220000-2222-2-2-2-2000000000000000000000000000000
χ2522222-2-222-2-2-2-2222-2-2-2-22-20020022-2-222-2-2000000002-20000000000000000000000000000002i−2i−2i2i00
χ2622222-2-222-2-2-2-2222-2-2-2-22-20020022-2-222-2-2000000002-2000000000000000000000000000000−2i2i2i−2i00
χ2722222-2-2-2-2-2-222222-2-2-2-22200-2002222-2-2-2-200000000-220000000000000022-2-20000000000-22000000
χ2822222-2-2-2-2-2-222222-2-2-2-22200-2002222-2-2-2-200000000-2200000000000000-2-22200000000002-2000000
χ292222-122222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ302222-122222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ312222-122222222-1-1-1-1-1-1-122-2-22-2-2-1-1-1-1-1-1-1-1-2-2112222-1-1111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ322222-122222222-1-1-1-1-1-1-122-2-22-2-2-1-1-1-1-1-1-1-1-2-211-2-2-2-2-1-111111111111111000022-1-1-1-1000000000000
χ332222-122-2-222-2-2-1-1-1-1-1-1-12-222-2-2-2-1-11111-1-12-2-1-10000111111-1-1−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ342222-122-2-222-2-2-1-1-1-1-1-1-12-222-2-2-2-1-11111-1-12-2-1-10000111111-1-1i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ352222-122-2-222-2-2-1-1-1-1-1-1-12-2-2-2-222-1-11111-1-1-2211000011-1-1-1-111−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ362222-122-2-222-2-2-1-1-1-1-1-1-12-2-2-2-222-1-11111-1-1-2211000011-1-1-1-111i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ372222-1-2-22222-2-2-1-1-11111-2222-2-2-21111-1-1-1-1-221100001-111-1-1-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ382222-1-2-22222-2-2-1-1-11111-2222-2-2-21111-1-1-1-1-221100001-111-1-1-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ392222-1-2-22222-2-2-1-1-11111-22-2-2-2221111-1-1-1-12-2-1-100001-1-1-11111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ402222-1-2-22222-2-2-1-1-11111-22-2-2-2221111-1-1-1-12-2-1-100001-1-1-11111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ412222-1-2-2-2-22222-1-1-11111-2-22222211-1-111-1-1-2-21122-2-2-11-1-111-1-1-1-1-1-1111100002-2-1-111000000000000
χ422222-1-2-2-2-22222-1-1-11111-2-22222211-1-111-1-1-2-211-2-222-11-1-111-1-11111-1-1-1-10000-2211-1-1000000000000
χ432222-1-2-2-2-22222-1-1-11111-2-2-2-22-2-211-1-111-1-122-1-122-2-2-1111-1-111-1-1-1-111110000-2211-1-1000000000000
χ442222-1-2-2-2-22222-1-1-11111-2-2-2-22-2-211-1-111-1-122-1-1-2-222-1111-1-1111111-1-1-1-100002-2-1-111000000000000
χ4522-2-222i−2i2i−2i002-22-2-22i2i−2i−2i0000000002-22i−2i000000−i2i22−200000000−i2i2−i2i22−22−22i−2i2-20000002−2−i2i200000000
χ4622-2-222i−2i2i−2i002-22-2-22i2i−2i−2i0000000002-22i−2i000000−i2i22−200000000−i2i2−i2i22−22−2−2i2i-22000000−22i2−i200000000
χ4722-2-222i−2i2i−2i002-22-2-22i2i−2i−2i0000000002-22i−2i000000i2−i2−2200000000i2−i2i2−i2−22−222i−2i2-2000000−22i2−i200000000
χ4822-2-222i−2i2i−2i002-22-2-22i2i−2i−2i0000000002-22i−2i000000i2−i2−2200000000i2−i2i2−i2−22−22−2i2i-220000002−2−i2i200000000
χ4922-2-22−2i2i−2i2i002-22-2-2−2i−2i2i2i0000000002-2−2i2i000000−i2i2−2200000000−i2i2−i2i2−22−222i−2i-220000002−2i2−i200000000
χ5022-2-22−2i2i−2i2i002-22-2-2−2i−2i2i2i0000000002-2−2i2i000000−i2i2−2200000000−i2i2−i2i2−22−22−2i2i2-2000000−22−i2i200000000
χ5122-2-22−2i2i−2i2i002-22-2-2−2i−2i2i2i0000000002-2−2i2i000000i2−i22−200000000i2−i2i2−i22−22−22i−2i-22000000−22−i2i200000000
χ5222-2-22−2i2i−2i2i002-22-2-2−2i−2i2i2i0000000002-2−2i2i000000i2−i22−200000000i2−i2i2−i22−22−2−2i2i2-20000002−2i2−i200000000
χ534444-24444-4-444-2-2-2-2-2-2-2-4-400-40022-2-2-2-2220000000022000000000000000000000000000000000000
χ544444-244-4-4-4-4-4-4-2-2-2-2-2-2-2-44004002222222200000000-2-2000000000000000000000000000000000000
χ554444-2-4-444-4-4-4-4-2-2-222224-400400-2-222-2-22200000000-22000000000000000000000000000000000000
χ564444-2-4-4-4-4-4-444-2-2-222224400-400-2-2-2-22222000000002-2000000000000000000000000000000000000
χ5744-4-444i−4i−4i4i00-444-4-44i4i−4i−4i000000000-44−4i4i000000000000000000000000000000000000000000000000
χ5844-4-44−4i4i4i−4i00-444-4-4−4i−4i4i4i000000000-444i−4i000000000000000000000000000000000000000000000000
χ5944-4-4-24i−4i4i−4i004-4-222−2i−2i2i2i000000000-22−2i2i000000−2i22i222−2200000000i2−i2i2−i2−22−220000000000000000000000
χ6044-4-4-24i−4i4i−4i004-4-222−2i−2i2i2i000000000-22−2i2i0000002i2−2i2−222200000000−i2i2−i2i22−22−20000000000000000000000
χ6144-4-4-24i−4i−4i4i00-44-222−2i−2i2i2i0000000002-22i−2i0000000000000000006−6−66i6−i6−i6i60000000000000000000000
χ6244-4-4-24i−4i−4i4i00-44-222−2i−2i2i2i0000000002-22i−2i000000000000000000−666−6−i6i6i6−i60000000000000000000000
χ6344-4-4-2−4i4i4i−4i00-44-2222i2i−2i−2i0000000002-2−2i2i0000000000000000006−6−66−i6i6i6−i60000000000000000000000
χ6444-4-4-2−4i4i4i−4i00-44-2222i2i−2i−2i0000000002-2−2i2i000000000000000000−666−6i6−i6−i6i60000000000000000000000
χ6544-4-4-2−4i4i−4i4i004-4-2222i2i−2i−2i000000000-222i−2i000000−2i22i2−222200000000i2−i2i2−i22−22−20000000000000000000000
χ6644-4-4-2−4i4i−4i4i004-4-2222i2i−2i−2i000000000-222i−2i0000002i2−2i222−2200000000−i2i2−i2i2−22−220000000000000000000000
χ674-44-4400004-400-4-440000000004i−4i0000004-400000000004i−4i0000000000000000000000000000000000
χ684-44-4400004-400-4-44000000000−4i4i0000004-40000000000−4i4i0000000000000000000000000000000000
χ694-44-440000-4400-4-440000004-4000000000-44000000000000004-4000000000000000000000000000000
χ704-44-440000-4400-4-44000000-44000000000-4400000000000000-44000000000000000000000000000000
χ714-44-4-200004-40022-2−2i32i3−2i32i3000004i−4i−2i32i30000-220000000000−2i2i23−2300000000000000000000000000000000
χ724-44-4-200004-40022-2−2i32i3−2i32i300000−4i4i−2i32i30000-2200000000002i−2i−232300000000000000000000000000000000
χ734-44-4-200004-40022-22i3−2i32i3−2i3000004i−4i2i3−2i30000-220000000000−2i2i−232300000000000000000000000000000000
χ744-44-4-200004-40022-22i3−2i32i3−2i300000−4i4i2i3−2i30000-2200000000002i−2i23−2300000000000000000000000000000000
χ754-44-4-20000-440022-2−2i32i3−2i32i3004-40002i3−2i300002-200−2i32i30000000000-22000000000000000000000000000000
χ764-44-4-20000-440022-2−2i32i3−2i32i300-440002i3−2i300002-2002i3−2i300000000002-2000000000000000000000000000000
χ774-44-4-20000-440022-22i3−2i32i3−2i3004-4000−2i32i300002-2002i3−2i30000000000-22000000000000000000000000000000
χ784-44-4-20000-440022-22i3−2i32i3−2i300-44000−2i32i300002-200−2i32i300000000002-2000000000000000000000000000000
χ798-8-88800000000-88-800000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-4000000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-8-88-4000000004-44−434343−430000000000000000000000000000000000000000000000000000000000000

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