Finite Group Databasebeta

← Group #10845487

Character table — Group #10845487

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444466666664444888812121212121212124444881212121212121212121224242424242424242244888844121212122444448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-11-1-11-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111
χ5111111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111
χ6111111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-11111-1-1
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
χ911111111111111111111-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-11-1-111-1-1-1-111-1-11-1
χ1011111111111111111111-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-111-11
χ1111111111111111111111-1-1-1-11111111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111111-111-1-1-111-1-1-1-1-1-11
χ1211111111111111111111-1-1-1-11111111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-1111111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-111-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-11-1-1111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1-11111-11
χ1611111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111111-1-1-1-11-1
χ17222222222-2-2-2-2222222222-2-20000-2-2-22222-20000000000-2-200000000000022-2-20000000000200-2000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-22222-20000000000-2-2000000000000-2-2220000000000-2002000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-200000000002200000000000022-2-20000000000-2002000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-2000000000022000000000000-2-2220000000000200-2000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-2221111-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-11111111111110000000022-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-11111-122-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-11111-1-2-222-2-2-1-1-1-1111111-1-1-1-11111000000002-2-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-122-2-222111111-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-1-2-22222-1-1-1-11111111111-1-1-1-100000000-2211-1-10000000000
χ2922-2-2-222-222-2-2222-2-22-2-2000000002-2-2000022i−2i00000000002i2i−2i−2i00000000000022-2-200000000002i−2i0000
χ3022-2-2-222-222-2-2222-2-22-2-2000000002-2-2000022i−2i00000000002i2i−2i−2i000000000000-2-2220000000000−2i2i0000
χ3122-2-2-222-222-2-2222-2-22-2-2000000002-2-200002−2i2i0000000000−2i−2i2i2i00000000000022-2-20000000000−2i2i0000
χ3222-2-2-222-222-2-2222-2-22-2-2000000002-2-200002−2i2i0000000000−2i−2i2i2i000000000000-2-22200000000002i−2i0000
χ332-22-2-2-22222-22-2-2-2222-2-20000000022-20000-2002-20022-2-20000000000000000002i−2i2i−2i00000002i−2i0000000
χ342-22-2-2-22222-22-2-2-2222-2-20000000022-20000-2002-20022-2-2000000000000000000−2i2i−2i2i0000000−2i2i0000000
χ352-22-2-2-22222-22-2-2-2222-2-20000000022-20000-200-2200-2-2220000000000000000002i−2i2i−2i0000000−2i2i0000000
χ362-22-2-2-22222-22-2-2-2222-2-20000000022-20000-200-2200-2-222000000000000000000−2i2i−2i2i00000002i−2i0000000
χ372-2-222-22-2222-2-2-2-2-2-22222-22-200002-2222-2-2-200000000002-200000000000000002i−2i−2i2i0000000000002i−2i00
χ382-2-222-22-2222-2-2-2-2-2-22222-22-200002-2222-2-2-200000000002-20000000000000000−2i2i2i−2i000000000000−2i2i00
χ392-2-222-22-2222-2-2-2-2-2-2222-22-2200002-22-2-222-20000000000-2200000000000000002i−2i−2i2i000000000000−2i2i00
χ402-2-222-22-2222-2-2-2-2-2-2222-22-2200002-22-2-222-20000000000-220000000000000000−2i2i2i−2i0000000000002i−2i00
χ412-2-222-22-22-2-222-2-2-2-22222-2-2222-2-2-22-222-2-2200002-20000-22000022-2-222-2-2000000000000000000000000
χ422-2-222-22-22-2-222-2-2-2-22222-2-22-2-222-22-222-2-220000-220000-220000-2-222-2-222000000000000000000000000
χ432-2-222-22-22-2-222-2-2-2-2222-222-222-2-2-22-2-2-22220000-2200002-2000022-2-2-2-222000000000000000000000000
χ442-2-222-22-22-2-222-2-2-2-2222-222-2-2-222-22-2-2-222200002-200002-20000-2-22222-2-2000000000000000000000000
χ452-2-222-22-2-1-2-2221111-1-1-12-2-2222-2-21-11-1-111-100002-2−i3i3−i3i31-1−i3i3−i3i3-1-111-1-1110000000000−i3i3−i3i30000000000
χ462-2-222-22-2-1-2-2221111-1-1-12-2-2222-2-21-11-1-111-100002-2i3−i3i3−i31-1i3−i3i3−i3-1-111-1-1110000000000i3−i3i3−i30000000000
χ472-2-222-22-2-1-2-2221111-1-1-12-2-22-2-2221-11-1-111-10000-22−i3i3−i3i31-1−i3i3−i3i311-1-111-1-10000000000i3−i3i3−i30000000000
χ482-2-222-22-2-1-2-2221111-1-1-12-2-22-2-2221-11-1-111-10000-22i3−i3i3−i31-1i3−i3i3−i311-1-111-1-10000000000−i3i3−i3i30000000000
χ492-2-222-22-2-1-2-2221111-1-1-1-222-222-2-21-1111-1-1-10000-22−i3i3−i3i3-11i3−i3i3−i3-1-11111-1-10000000000−i3i3i3−i30000000000
χ502-2-222-22-2-1-2-2221111-1-1-1-222-222-2-21-1111-1-1-10000-22i3−i3i3−i3-11−i3i3−i3i3-1-11111-1-10000000000i3−i3−i3i30000000000
χ512-2-222-22-2-1-2-2221111-1-1-1-222-2-2-2221-1111-1-1-100002-2−i3i3−i3i3-11i3−i3i3−i311-1-1-1-1110000000000i3−i3−i3i30000000000
χ522-2-222-22-2-1-2-2221111-1-1-1-222-2-2-2221-1111-1-1-100002-2i3−i3i3−i3-11−i3i3−i3i311-1-1-1-1110000000000−i3i3i3−i30000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000222-2-2-2-22000000000022000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000222222220000000000-2-2000000000000000000000000000000000000
χ55444-44-4-4-4400004-44-4-4-44000022−2222−2200000000000000000000000022−2222−220000000000000000000000000000
χ56444-44-4-4-4400004-44-4-4-440000−2222−2222000000000000000000000000−2222−22220000000000000000000000000000
χ57444-44-4-4-4-20000-22-2222-2000022−2222−2200023−2323−2300000000000000000−22−226−66−6000000000000000000000000
χ58444-44-4-4-4-20000-22-2222-2000022−2222−22000−2323−232300000000000000000−22−22−66−66000000000000000000000000
χ59444-44-4-4-4-20000-22-2222-20000−2222−222200023−2323−23000000000000000002−22−2−66−66000000000000000000000000
χ60444-44-4-4-4-20000-22-2222-20000−2222−2222000−2323−2323000000000000000002−22−26−66−6000000000000000000000000
χ6144-44-4-4-44400004-4-44-44-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ6244-44-4-4-44400004-4-44-44-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ6344-4-4-444-44-444-444-4-44-4-400000000-4440000-4000000000000000000000000000000000000000000000000
χ6444-4-4-444-4-24-4-44-2-222-22200000000-2220000-24i−4i0000000000−2i−2i2i2i00000000000000000000000000000000
χ6544-4-4-444-4-24-4-44-2-222-22200000000-2220000-2−4i4i00000000002i2i−2i−2i00000000000000000000000000000000
χ6644-4-4-444-4-2-444-4-2-222-222000000002-2-200002000000−2i32i32i3−2i300000000000000000000000000000000000000
χ6744-4-4-444-4-2-444-4-2-222-222000000002-2-2000020000002i3−2i3−2i32i300000000000000000000000000000000000000
χ684-444-44-4-440000-444-4-44-400000000000000000000000000000000000000004-40000000000000000000000
χ694-444-44-4-440000-444-4-44-40000000000000000000000000000000000000000-440000000000000000000000
χ704-44-4-4-4444-44-44-4-4444-4-400000000-4-4400004000000000000000000000000000000000000000000000000
χ714-44-4-4-444-24-44-422-2-2-22200000000-2-2200002004-400-2-22200000000000000000000000000000000000000
χ724-44-4-4-444-24-44-422-2-2-22200000000-2-220000200-440022-2-200000000000000000000000000000000000000
χ734-44-4-4-444-2-44-4422-2-2-2220000000022-20000-200000000000023−23−232300000000000000000000000000000000
χ744-44-4-4-444-2-44-4422-2-2-2220000000022-20000-2000000000000−232323−2300000000000000000000000000000000
χ754-4-444-44-4-244-4-42222-2-2-24-44-40000-22-2-2-22220000000000-22000000000000000000000000000000000000
χ764-4-444-44-4-244-4-42222-2-2-2-44-440000-22-222-2-2200000000002-2000000000000000000000000000000000000
χ774-4-4-444-4440000-44-44-4-44000022−22−222200000000000000000000000022−22−22220000000000000000000000000000
χ784-4-4-444-4440000-44-44-4-440000−222222−22000000000000000000000000−222222−220000000000000000000000000000
χ794-4-4-444-44-200002-22-222-2000022−22−222200023−23−232300000000000000000−222−26−6−66000000000000000000000000
χ804-4-4-444-44-200002-22-222-2000022−22−2222000−232323−2300000000000000000−222−2−666−6000000000000000000000000
χ814-4-4-444-44-200002-22-222-20000−222222−2200023−23−2323000000000000000002−2−22−666−6000000000000000000000000
χ824-4-4-444-44-200002-22-222-20000−222222−22000−232323−23000000000000000002−2−226−6−66000000000000000000000000
χ8388-88-8-8-88-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000

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