Finite Group Databasebeta

← Group #10846052

Character table — Group #10846052

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order1222222234444666666644448888121212121212121222446666881212121212122424242424242424224488882266662444448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-11-1-11-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111
χ5111111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111
χ6111111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-11111-1-1
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111
χ911111111111111111111-1-1-1-11111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-111-1-1-1-1-1-111-1-1-11
χ1011111111111111111111-1-1-1-11111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11111-1-1111-1
χ1111111111111111111111-1-1-1-11111111-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-11-1-111-111-1-1-1-1-11-1
χ1211111111111111111111-1-1-1-11111111-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111111-11
χ1311111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-111-1-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-1111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-1-1-1-111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111-111-1-11111-1-1-1-1-11
χ17222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-200000000002200000000000022-2-20000000000200-2000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2000000000022000000000000-2-2220000000000-2002000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-22222-20000000000-2-200000000000022-2-20000000000-2002000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-22222-20000000000-2-2000000000000-2-2220000000000200-2000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-2111122-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-2-211110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-1-11111111111110000000022-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-11111-122-2-2-1-1-1-1-2-2111111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-11111-1-2-2221111-2-211-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-122-2-2-1-1-1-1221111111111-1-1-1-100000000-2211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-1-2-22211112211-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2922-2-22-22-222-22-222-2-22-2-20000000022-20000-2002i−2i000000002i2i−2i−2i0000000000002i2i−2i−2i00000002-20000000
χ3022-2-22-22-222-22-222-2-22-2-20000000022-20000-2002i−2i000000002i2i−2i−2i000000000000−2i−2i2i2i0000000-220000000
χ3122-2-22-22-222-22-222-2-22-2-20000000022-20000-200−2i2i00000000−2i−2i2i2i0000000000002i2i−2i−2i0000000-220000000
χ3222-2-22-22-222-22-222-2-22-2-20000000022-20000-200−2i2i00000000−2i−2i2i2i000000000000−2i−2i2i2i00000002-20000000
χ332-222-2-22-2222-2-2-2-2-2-22222-22-200002-2222-2-2-200000000002-200000000000000002i−2i2i−2i0000000000002i−2i00
χ342-222-2-22-2222-2-2-2-2-2-22222-22-200002-2222-2-2-200000000002-20000000000000000−2i2i−2i2i000000000000−2i2i00
χ352-222-2-22-2222-2-2-2-2-2-2222-22-2200002-22-2-222-20000000000-2200000000000000002i−2i2i−2i000000000000−2i2i00
χ362-222-2-22-2222-2-2-2-2-2-2222-22-2200002-22-2-222-20000000000-220000000000000000−2i2i−2i2i0000000000002i−2i00
χ372-222-2-22-22-2-222-2-2-2-22222-2-2222-2-2-22-2-2-2222000000002-22-2000022-2-222-2-2000000000000000000000000
χ382-222-2-22-22-2-222-2-2-2-22222-2-22-2-222-22-2-2-222200000000-222-20000-2-222-2-222000000000000000000000000
χ392-222-2-22-22-2-222-2-2-2-2222-222-222-2-2-22-222-2-2200000000-22-22000022-2-2-2-222000000000000000000000000
χ402-222-2-22-22-2-222-2-2-2-2222-222-2-2-222-22-222-2-22000000002-2-220000-2-22222-2-2000000000000000000000000
χ412-222-2-22-2-1-2-2221111-1-1-12-2-2222-2-21-1111-1-1-10000−i3−i3i3i32-2-11−i3i3−i3i3-1-111-1-1110000000000−i3i3−i3i30000000000
χ422-222-2-22-2-1-2-2221111-1-1-12-2-2222-2-21-1111-1-1-10000i3i3−i3−i32-2-11i3−i3i3−i3-1-111-1-1110000000000i3−i3i3−i30000000000
χ432-222-2-22-2-1-2-2221111-1-1-12-2-22-2-2221-1111-1-1-10000−i3−i3i3i3-22-11−i3i3−i3i311-1-111-1-10000000000i3−i3i3−i30000000000
χ442-222-2-22-2-1-2-2221111-1-1-12-2-22-2-2221-1111-1-1-10000i3i3−i3−i3-22-11i3−i3i3−i311-1-111-1-10000000000−i3i3−i3i30000000000
χ452-222-2-22-2-1-2-2221111-1-1-1-222-222-2-21-11-1-111-10000−i3−i3i3i3-221-1i3−i3i3−i3-1-11111-1-10000000000−i3i3i3−i30000000000
χ462-222-2-22-2-1-2-2221111-1-1-1-222-222-2-21-11-1-111-10000i3i3−i3−i3-221-1−i3i3−i3i3-1-11111-1-10000000000i3−i3−i3i30000000000
χ472-222-2-22-2-1-2-2221111-1-1-1-222-2-2-2221-11-1-111-10000−i3−i3i3i32-21-1i3−i3i3−i311-1-1-1-1110000000000i3−i3−i3i30000000000
χ482-222-2-22-2-1-2-2221111-1-1-1-222-2-2-2221-11-1-111-10000i3i3−i3−i32-21-1−i3i3−i3i311-1-1-1-1110000000000−i3i3i3−i30000000000
χ492-2-2-2-222222-2-22-2-2222-2-2000000002-2-2000022-2002-22-2000000000000000000002-2-2200000000002-20000
χ502-2-2-2-222222-2-22-2-2222-2-2000000002-2-2000022-2002-22-200000000000000000000-222-20000000000-220000
χ512-2-2-2-222222-2-22-2-2222-2-2000000002-2-200002-2200-22-22000000000000000000002-2-220000000000-220000
χ522-2-2-2-222222-2-22-2-2222-2-2000000002-2-200002-2200-22-2200000000000000000000-222-200000000002-20000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000222222220000000000-2-2000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000222-2-2-2-22000000000022000000000000000000000000000000000000
χ55444-4-44-4-4400004-44-4-44-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ56444-4-44-4-4400004-44-4-44-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ5744-44-4-4-44400004-4-44-4-44000022−2222−2200000000000000000000000022−2222−220000000000000000000000000000
χ5844-44-4-4-44400004-4-44-4-440000−2222−2222000000000000000000000000−2222−22220000000000000000000000000000
χ5944-44-4-4-44-20000-222-222-2000022−2222−22000−2i32i3−2i32i300000000000000000−22−22i6−i6i6−i6000000000000000000000000
χ6044-44-4-4-44-20000-222-222-2000022−2222−220002i3−2i32i3−2i300000000000000000−22−22−i6i6−i6i6000000000000000000000000
χ6144-44-4-4-44-20000-222-222-20000−2222−2222000−2i32i3−2i32i3000000000000000002−22−2−i6i6−i6i6000000000000000000000000
χ6244-44-4-4-44-20000-222-222-20000−2222−22220002i3−2i32i3−2i3000000000000000002−22−2i6−i6i6−i6000000000000000000000000
χ6344-4-44-44-44-44-4444-4-44-4-400000000-4-4400004000000000000000000000000000000000000000000000000
χ6444-4-44-44-4-24-44-4-2-222-22200000000-2-2200002004i−4i00000000−2i−2i2i2i00000000000000000000000000000000
χ6544-4-44-44-4-24-44-4-2-222-22200000000-2-220000200−4i4i000000002i2i−2i−2i00000000000000000000000000000000
χ6644-4-44-44-4-2-44-44-2-222-2220000000022-20000-20000−2i32i32i3−2i30000000000000000000000000000000000000000
χ6744-4-44-44-4-2-44-44-2-222-2220000000022-20000-200002i3−2i3−2i32i30000000000000000000000000000000000000000
χ684-444-4-44-4-244-4-42222-2-2-24-44-40000-22-2-2-22220000000000-22000000000000000000000000000000000000
χ694-444-4-44-4-244-4-42222-2-2-2-44-440000-22-222-2-2200000000002-2000000000000000000000000000000000000
χ704-44-44-4-4440000-44-44-44-400000000000000000000000000000000000000004-40000000000000000000000
χ714-44-44-4-4440000-44-44-44-40000000000000000000000000000000000000000-440000000000000000000000
χ724-4-4444-4-440000-444-4-4-44000022−22−222200000000000000000000000022−22−22220000000000000000000000000000
χ734-4-4444-4-440000-444-4-4-440000−222222−22000000000000000000000000−222222−220000000000000000000000000000
χ744-4-4444-4-4-200002-2-2222-2000022−22−2222000−2i32i32i3−2i300000000000000000−222−2−i6i6i6−i6000000000000000000000000
χ754-4-4444-4-4-200002-2-2222-2000022−22−22220002i3−2i3−2i32i300000000000000000−222−2i6−i6−i6i6000000000000000000000000
χ764-4-4444-4-4-200002-2-2222-20000−222222−22000−2i32i32i3−2i3000000000000000002−2−22i6−i6−i6i6000000000000000000000000
χ774-4-4444-4-4-200002-2-2222-20000−222222−220002i3−2i3−2i32i3000000000000000002−2−22−i6i6i6−i6000000000000000000000000
χ784-4-4-4-44444-444-4-4-4444-4-400000000-4440000-4000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-24-4-4422-2-2-22200000000-2220000-24-400-22-220000000000000000000000000000000000000000
χ804-4-4-4-4444-24-4-4422-2-2-22200000000-2220000-2-44002-22-20000000000000000000000000000000000000000
χ814-4-4-4-4444-2-444-422-2-2-222000000002-2-20000200000000000023−23−232300000000000000000000000000000000
χ824-4-4-4-4444-2-444-422-2-2-222000000002-2-200002000000000000−232323−2300000000000000000000000000000000
χ83888-8-88-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-88-8-88-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000

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