Finite Group Databasebeta

← Group #10827620

Character table — Group #10827620

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212121212121616161624242424242424244848
order12222222344446666666224466661212121244444444888812121212121212121212242424242424242422444444121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111
χ911111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-11-111-1-11-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-11-1-111-11
χ1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1111-1
χ1211111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1111-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-11-1-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111-1111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111-111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-11-1-1111-1
χ17222222222-2-2-2-2222222222-2-22222-2-2-2-2000000000000-2-2000000000000000022-2-20000000000-22000000
χ18222222222-2-2-2-2222222222-2-22222-2-2-2-2000000000000-2-20000000000000000-2-22200000000002-2000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-200000000000022000000000000000022220000000000-2-2000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2-2-2000000000022000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000011110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1111111111111111100000000-1-1-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000000011110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-222-2-222-2-211-1-1-1-11111-1-1-1-1111100000000-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-2-2-222-2-22211-1-1-1-111111111-1-1-1-10000000011-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-100000000-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-111110000000011-1-10000000000
χ2922-22-2-22-2222-2-222-2-2-2-22000000002-22-2002-20000000000000022-2-20000000000002i2i−2i−2i00000000002i−2i00
χ3022-22-2-22-2222-2-222-2-2-2-22000000002-22-2002-20000000000000022-2-2000000000000−2i−2i2i2i0000000000−2i2i00
χ3122-22-2-22-2222-2-222-2-2-2-22000000002-22-200-2200000000000000-2-2220000000000002i2i−2i−2i0000000000−2i2i00
χ3222-22-2-22-2222-2-222-2-2-2-22000000002-22-200-2200000000000000-2-222000000000000−2i−2i2i2i00000000002i−2i00
χ332-22-22-22-222-22-2-2-222-2-22000000002-2-222-200000000000022-2-200000000000000002i−2i2i−2i000000002i−2i0000
χ342-22-22-22-222-22-2-2-222-2-22000000002-2-222-200000000000022-2-20000000000000000−2i2i−2i2i00000000−2i2i0000
χ352-22-22-22-222-22-2-2-222-2-22000000002-2-22-22000000000000-2-22200000000000000002i−2i2i−2i00000000−2i2i0000
χ362-22-22-22-222-22-2-2-222-2-22000000002-2-22-22000000000000-2-2220000000000000000−2i2i−2i2i000000002i−2i0000
χ372-2-2-2-222222-2-22-2-2-2-22222-22-222-2-222-2-20000000000002-2000000000000000000002-2-2200002-200000000
χ382-2-2-2-222222-2-22-2-2-2-22222-22-222-2-222-2-20000000000002-200000000000000000000-222-20000-2200000000
χ392-2-2-2-222222-2-22-2-2-2-2222-22-22-2-22222-2-2000000000000-22000000000000000000002-2-220000-2200000000
χ402-2-2-2-222222-2-22-2-2-2-2222-22-22-2-22222-2-2000000000000-2200000000000000000000-222-200002-200000000
χ412-2-2-2-22222-222-2-2-2-2-22222-2-2222-2-2-2-22200002-22-20000-220000000000000000000000002-22-20000000000
χ422-2-2-2-22222-222-2-2-2-2-22222-2-2222-2-2-2-2220000-22-220000-22000000000000000000000000-22-220000000000
χ432-2-2-2-22222-222-2-2-2-2-2222-222-2-2-222-2-22200002-2-2200002-20000000000000000000000002-2-220000000000
χ442-2-2-2-22222-222-2-2-2-2-2222-222-2-2-222-2-2220000-222-200002-2000000000000000000000000-222-20000000000
χ452-2-2-2-2222-1-222-21111-1-1-12-2-22-1-11111-1-100002-22-200001-1−i3i3−i3i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3i300000000-11-110000000000
χ462-2-2-2-2222-1-222-21111-1-1-12-2-22-1-11111-1-100002-22-200001-1i3−i3i3−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3−i300000000-11-110000000000
χ472-2-2-2-2222-1-222-21111-1-1-12-2-22-1-11111-1-10000-22-2200001-1−i3i3−i3i3−i3i3−i3i3i3i3−i3−i3i3i3−i3−i3000000001-11-10000000000
χ482-2-2-2-2222-1-222-21111-1-1-12-2-22-1-11111-1-10000-22-2200001-1i3−i3i3−i3i3−i3i3−i3−i3−i3i3i3−i3−i3i3i3000000001-11-10000000000
χ492-2-2-2-2222-1-222-21111-1-1-1-222-211-1-111-1-100002-2-220000-11−i3i3−i3i3i3−i3i3−i3−i3−i3i3i3i3i3−i3−i300000000-111-10000000000
χ502-2-2-2-2222-1-222-21111-1-1-1-222-211-1-111-1-100002-2-220000-11i3−i3i3−i3−i3i3−i3i3i3i3−i3−i3−i3−i3i3i300000000-111-10000000000
χ512-2-2-2-2222-1-222-21111-1-1-1-222-211-1-111-1-10000-222-20000-11−i3i3−i3i3i3−i3i3−i3i3i3−i3−i3−i3−i3i3i3000000001-1-110000000000
χ522-2-2-2-2222-1-222-21111-1-1-1-222-211-1-111-1-10000-222-20000-11i3−i3i3−i3−i3i3−i3i3−i3−i3i3i3i3i3−i3−i3000000001-1-110000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-222220000000000002200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422222222000000000000-2-200000000000000000000000000000000000000
χ55444-4-4-4-44400004-44-4-44-40000000000000000000000000000000000000000004-400000000000000000000
χ56444-4-4-4-44400004-44-4-44-4000000000000000000000000000000000000000000-4400000000000000000000
χ5744-44-4-44-44-4-44444-4-4-4-4400000000-44-440000000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-244-4-4-2-22222-200000000-22-22004-400000000000000-2-222000000000000000000000000000000
χ5944-44-4-44-4-244-4-4-2-22222-200000000-22-2200-440000000000000022-2-2000000000000000000000000000000
χ6044-44-4-44-4-2-4-444-2-22222-2000000002-22-200000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ6144-44-4-44-4-2-4-444-2-22222-2000000002-22-2000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ6244-4-444-4-4400004-4-444-4-4000000000000000000000022−220000000000000022−2222−220000000000000000000000
χ6344-4-444-4-4400004-4-444-4-40000000000000000000000−222200000000000000−2222−22220000000000000000000000
χ6444-4-444-4-4-20000-222-2-2220000−2i32i3−2i32i30000000000000022−220000000000i6−i6i6−i6−22−220000000000000000000000
χ6544-4-444-4-4-20000-222-2-2220000−2i32i3−2i32i300000000000000−22220000000000−i6i6−i6i62−22−20000000000000000000000
χ6644-4-444-4-4-20000-222-2-22200002i3−2i32i3−2i30000000000000022−220000000000−i6i6−i6i6−22−220000000000000000000000
χ6744-4-444-4-4-20000-222-2-22200002i3−2i32i3−2i300000000000000−22220000000000i6−i6i6−i62−22−20000000000000000000000
χ684-444-44-4-440000-444-44-4-40000000000000000000022−2200000000000022−22−222200000000000000000000000000
χ694-444-44-4-440000-444-44-4-400000000000000000000−2222000000000000−222222−2200000000000000000000000000
χ704-444-44-4-4-200002-2-22-2220000−2i32i32i3−2i300000000000022−22000000000000−222−2i6−i6−i6i60000000000000000000000
χ714-444-44-4-4-200002-2-22-2220000−2i32i32i3−2i3000000000000−22220000000000002−2−22−i6i6i6−i60000000000000000000000
χ724-444-44-4-4-200002-2-22-22200002i3−2i3−2i32i300000000000022−22000000000000−222−2−i6i6i6−i60000000000000000000000
χ734-444-44-4-4-200002-2-22-22200002i3−2i3−2i32i3000000000000−22220000000000002−2−22i6−i6−i6i60000000000000000000000
χ744-44-44-44-44-44-44-4-444-4-4400000000-444-40000000000000000000000000000000000000000000000000000
χ754-44-44-44-4-24-44-422-2-222-200000000-222-24-4000000000000-2-2220000000000000000000000000000000000
χ764-44-44-44-4-24-44-422-2-222-200000000-222-2-4400000000000022-2-20000000000000000000000000000000000
χ774-44-44-44-4-2-44-4422-2-222-2000000002-2-22000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ784-44-44-44-4-2-44-4422-2-222-2000000002-2-220000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ794-4-444-4-4440000-44-44-44-4000000000000000000000000000000000000000000004i−4i000000000000000000
χ804-4-444-4-4440000-44-44-44-400000000000000000000000000000000000000000000−4i4i000000000000000000
χ814-4-4-4-4444-24-4-442222-2-2-24-44-4-2-222-2-222000000000000-2200000000000000000000000000000000000000
χ824-4-4-4-4444-24-4-442222-2-2-2-44-4422-2-2-2-2220000000000002-200000000000000000000000000000000000000
χ83888-8-8-8-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000

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