Finite Group Databasebeta

← Group #10844879

Character table — Group #10844879

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444466666664444888812121212121212124444881212121212121212121224242424242424244444888844121212124444448824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111
χ911111111111111111111-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-111-1-1-1-111-1-1-1-11-1
χ1011111111111111111111-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-11
χ1111111111111111111111-1-1-1-11111111-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-11-1-111-1-1-1-111-1-1-11
χ1211111111111111111111-1-1-1-11111111-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1-111111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111111-1-1-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-1-111-1-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-111-1-111-1-11-1
χ17222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-200000022000000000000000022-2-200000000002-200000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2000000220000000000000000-2-2220000000000-2200000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-22222-2000000-2-2000000000000000022-2-20000000000-2200000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-22222-2000000-2-20000000000000000-2-22200000000002-200000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
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
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-11111-122-2-2-2-211-1-1-1-11111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-11111-1-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-122-2-22211-1-1-1-111111111-1-1-1-100000000-2211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-1-2-22222111111-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2922-22-2-22-222-2-222-22-2-22-2000000002-2-200002002i−2i000000002i2i−2i−2i0000000000002i2i−2i−2i00000000002-20000
χ3022-22-2-22-222-2-222-22-2-22-2000000002-2-200002002i−2i000000002i2i−2i−2i000000000000−2i−2i2i2i0000000000-220000
χ3122-22-2-22-222-2-222-22-2-22-2000000002-2-20000200−2i2i00000000−2i−2i2i2i0000000000002i2i−2i−2i0000000000-220000
χ3222-22-2-22-222-2-222-22-2-22-2000000002-2-20000200−2i2i00000000−2i−2i2i2i000000000000−2i−2i2i2i00000000002-20000
χ332-22-22-22-222-22-2-222-2-2-220000000022-20000-22i−2i0000002i2i−2i−2i00000000000000002-22-2000000002i−2i000000
χ342-22-22-22-222-22-2-222-2-2-220000000022-20000-22i−2i0000002i2i−2i−2i0000000000000000-22-2200000000−2i2i000000
χ352-22-22-22-222-22-2-222-2-2-220000000022-20000-2−2i2i000000−2i−2i2i2i00000000000000002-22-200000000−2i2i000000
χ362-22-22-22-222-22-2-222-2-2-220000000022-20000-2−2i2i000000−2i−2i2i2i0000000000000000-22-22000000002i−2i000000
χ372-2-2-2-2222222-2-2-2-2222-2-22-22-200002-2222-2-2-20000002-2000000000000000000002i−2i−2i2i0000000000002i−2i00
χ382-2-2-2-2222222-2-2-2-2222-2-22-22-200002-2222-2-2-20000002-200000000000000000000−2i2i2i−2i000000000000−2i2i00
χ392-2-2-2-2222222-2-2-2-2222-2-2-22-2200002-22-2-222-2000000-22000000000000000000002i−2i−2i2i000000000000−2i2i00
χ402-2-2-2-2222222-2-2-2-2222-2-2-22-2200002-22-2-222-2000000-2200000000000000000000−2i2i2i−2i0000000000002i−2i00
χ412-2-2-2-22222-2-222-2-2222-2-22-2-2222-2-2-22-2-2-222200002-22-20000000022-2-222-2-2000000000000000000000000
χ422-2-2-2-22222-2-222-2-2222-2-22-2-22-2-222-22-2-2-22220000-222-200000000-2-222-2-222000000000000000000000000
χ432-2-2-2-22222-2-222-2-2222-2-2-222-222-2-2-22-222-2-220000-22-220000000022-2-2-2-222000000000000000000000000
χ442-2-2-2-22222-2-222-2-2222-2-2-222-2-2-222-22-222-2-2200002-2-2200000000-2-22222-2-2000000000000000000000000
χ452-2-2-2-2222-1-2-22211-1-1-1112-2-2222-2-21-1111-1-1-100002-2-113−33−33−33−3-1-111-1-11100000000003−33−30000000000
χ462-2-2-2-2222-1-2-22211-1-1-1112-2-2222-2-21-1111-1-1-100002-2-11−33−33−33−33-1-111-1-1110000000000−33−330000000000
χ472-2-2-2-2222-1-2-22211-1-1-1112-2-22-2-2221-1111-1-1-10000-22-113−33−33−33−311-1-111-1-10000000000−33−330000000000
χ482-2-2-2-2222-1-2-22211-1-1-1112-2-22-2-2221-1111-1-1-10000-22-11−33−33−33−3311-1-111-1-100000000003−33−30000000000
χ492-2-2-2-2222-1-2-22211-1-1-111-222-222-2-21-11-1-111-10000-221-13−33−3−33−33-1-11111-1-100000000003−3−330000000000
χ502-2-2-2-2222-1-2-22211-1-1-111-222-222-2-21-11-1-111-10000-221-1−33−333−33−3-1-11111-1-10000000000−333−30000000000
χ512-2-2-2-2222-1-2-22211-1-1-111-222-2-2-2221-11-1-111-100002-21-13−33−3−33−3311-1-1-1-1110000000000−333−30000000000
χ522-2-2-2-2222-1-2-22211-1-1-111-222-2-2-2221-11-1-111-100002-21-1−33−333−33−311-1-1-1-11100000000003−3−330000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4000022222222000000-2-20000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000222-2-2-2-22000000220000000000000000000000000000000000000000
χ55444-4-4-4-444000044-44-4-4-4000022−2222−2200000000000000000000000022−2222−220000000000000000000000000000
χ56444-4-4-4-444000044-44-4-4-40000−2222−2222000000000000000000000000−2222−22220000000000000000000000000000
χ57444-4-4-4-44-20000-2-22-2222000022−2222−22000−2i32i3−2i32i300000000000000000−22−22i6−i6i6−i6000000000000000000000000
χ58444-4-4-4-44-20000-2-22-2222000022−2222−220002i3−2i32i3−2i300000000000000000−22−22−i6i6−i6i6000000000000000000000000
χ59444-4-4-4-44-20000-2-22-22220000−2222−2222000−2i32i3−2i32i3000000000000000002−22−2−i6i6−i6i6000000000000000000000000
χ60444-4-4-4-44-20000-2-22-22220000−2222−22220002i3−2i32i3−2i3000000000000000002−22−2i6−i6i6−i6000000000000000000000000
χ6144-44-4-44-44-444-44-44-4-44-400000000-4440000-4000000000000000000000000000000000000000000000000
χ6244-44-4-44-4-24-4-44-22-222-2200000000-2220000-2004i−4i00000000−2i−2i2i2i00000000000000000000000000000000
χ6344-44-4-44-4-24-4-44-22-222-2200000000-2220000-200−4i4i000000002i2i−2i−2i00000000000000000000000000000000
χ6444-44-4-44-4-2-444-4-22-222-22000000002-2-20000200000000−2i32i32i3−2i3000000000000000000000000000000000000
χ6544-44-4-44-4-2-444-4-22-222-22000000002-2-200002000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ6644-4-444-4-4400004-4-4-44-440000000000000000000000000000000000000000004i−4i00000000000000000000
χ6744-4-444-4-4400004-4-4-44-44000000000000000000000000000000000000000000−4i4i00000000000000000000
χ684-444-44-4-440000-44-4-444-400000000000000000000000000000000000000004-40000000000000000000000
χ694-444-44-4-440000-44-4-444-40000000000000000000000000000000000000000-440000000000000000000000
χ704-44-44-44-44-44-44-444-4-4-4400000000-4-4400004000000000000000000000000000000000000000000000000
χ714-44-44-44-4-24-44-42-2-2222-200000000-2-22000024i−4i000000−2i−2i2i2i000000000000000000000000000000000000
χ724-44-44-44-4-24-44-42-2-2222-200000000-2-2200002−4i4i0000002i2i−2i−2i000000000000000000000000000000000000
χ734-44-44-44-4-2-44-442-2-2222-20000000022-20000-2000000000000−2i32i32i3−2i300000000000000000000000000000000
χ744-44-44-44-4-2-44-442-2-2222-20000000022-20000-20000000000002i3−2i3−2i32i300000000000000000000000000000000
χ754-4-444-4-4440000-4-4-44-444000022−22−222200000000000000000000000022−22−22220000000000000000000000000000
χ764-4-444-4-4440000-4-4-44-4440000−222222−22000000000000000000000000−222222−220000000000000000000000000000
χ774-4-444-4-44-20000222-22-2-2000022−22−2222000−2i32i32i3−2i300000000000000000−222−2−i6i6i6−i6000000000000000000000000
χ784-4-444-4-44-20000222-22-2-2000022−22−22220002i3−2i3−2i32i300000000000000000−222−2i6−i6−i6i6000000000000000000000000
χ794-4-444-4-44-20000222-22-2-20000−222222−22000−2i32i32i3−2i3000000000000000002−2−22i6−i6−i6i6000000000000000000000000
χ804-4-444-4-44-20000222-22-2-20000−222222−220002i3−2i3−2i32i3000000000000000002−2−22−i6i6i6−i6000000000000000000000000
χ814-4-4-4-4444-244-4-422-2-2-2224-44-40000-22-2-2-2222000000-220000000000000000000000000000000000000000
χ824-4-4-4-4444-244-4-422-2-2-222-44-440000-22-222-2-220000002-20000000000000000000000000000000000000000
χ8388-8-888-8-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000

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