Finite Group Databasebeta

← Group #10849320

Character table — Group #10849320

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212121212121616161624242424242424244848
order12222222344446666666444412121212121212122222444488881212121212121212121224242424242424244444444466664444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ911111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-11-111-1-11-1
χ1011111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-11-1-111-11
χ1111111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-11-1-1-111-11
χ1211111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1111-1-11-1
χ1311111111111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1111-1-1-11
χ1411111111111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1-1111-1
χ1511111111111111111111-1-1-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-11-1-1111-1
χ1611111111111111111111-1-1-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1-11
χ17222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-200000000000022000000000000000000002222000000-2-2000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-20000000000002200000000000000000000-2-2-2-200000022000000
χ19222222222-2-2-2-22222222-2-222-2-2-22222-2000000000000-2-20000000000000000000022-2-2000000-22000000
χ20222222222-2-2-2-22222222-2-222-2-2-22222-2000000000000-2-200000000000000000000-2-2220000002-2000000
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1111111111111111100000000-1-1-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000011110000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-122-2-222-2-222-2-211-1-1-1-11111-1-1-1-1111100000000-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-122-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-100000000-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-1-2-22222-2-2-2-22211-1-1-1-111111111-1-1-1-10000000011-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-1-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-111110000000011-1-10000000000
χ2922-22-22-2-22-222-22-22-2-22-200002-2-2000020000002-2000000000022-2-2000000002i2i−2i−2i000000000000002i−2i00
χ3022-22-22-2-22-222-22-22-2-22-200002-2-2000020000002-2000000000022-2-200000000−2i−2i2i2i00000000000000−2i2i00
χ3122-22-22-2-22-222-22-22-2-22-200002-2-200002000000-220000000000-2-222000000002i2i−2i−2i00000000000000−2i2i00
χ3222-22-22-2-22-222-22-22-2-22-200002-2-200002000000-220000000000-2-22200000000−2i−2i2i2i000000000000002i−2i00
χ332-22-222-2-22-22-22-222-2-2-220000-22-20000200002-20000000022-2-20000000000002i−2i2i−2i0000000000002i−2i0000
χ342-22-222-2-22-22-22-222-2-2-220000-22-20000200002-20000000022-2-2000000000000−2i2i−2i2i000000000000−2i2i0000
χ352-22-222-2-22-22-22-222-2-2-220000-22-2000020000-2200000000-2-2220000000000002i−2i2i−2i000000000000−2i2i0000
χ362-22-222-2-22-22-22-222-2-2-220000-22-2000020000-2200000000-2-222000000000000−2i2i−2i2i0000000000002i−2i0000
χ372-2-2-2-2222222-2-2-2-2222-2-22-22-2-2-2222-2-220000000000002-200000000000000002-2-22000000002-200000000
χ382-2-2-2-2222222-2-2-2-2222-2-22-22-2-2-2222-2-220000000000002-20000000000000000-222-200000000-2200000000
χ392-2-2-2-2222222-2-2-2-2222-2-2-22-22-2-22-2-2222000000000000-2200000000000000002-2-2200000000-2200000000
χ402-2-2-2-2222222-2-2-2-2222-2-2-22-22-2-22-2-2222000000000000-220000000000000000-222-2000000002-200000000
χ412-2-2-2-22222-2-222-2-2222-2-22-2-2222-2-2-222-22-22-2000000002-20000000000000000000000002-22-20000000000
χ422-2-2-2-22222-2-222-2-2222-2-22-2-2222-2-2-222-2-22-22000000002-2000000000000000000000000-22-220000000000
χ432-2-2-2-22222-2-222-2-2222-2-2-222-222-222-2-2-22-2-2200000000-220000000000000000000000002-2-220000000000
χ442-2-2-2-22222-2-222-2-2222-2-2-222-222-222-2-2-2-222-200000000-22000000000000000000000000-222-20000000000
χ452-2-2-2-2222-1-2-22211-1-1-1112-2-22-1-1111-1-112-22-200000000-113−33−33−33−333−3−333−3−300000000-11-110000000000
χ462-2-2-2-2222-1-2-22211-1-1-1112-2-22-1-1111-1-112-22-200000000-11−33−33−33−33−3−333−3−33300000000-11-110000000000
χ472-2-2-2-2222-1-2-22211-1-1-1112-2-22-1-1111-1-11-22-2200000000-113−33−33−33−3−3−333−3−333000000001-11-10000000000
χ482-2-2-2-2222-1-2-22211-1-1-1112-2-22-1-1111-1-11-22-2200000000-11−33−33−33−3333−3−333−3−3000000001-11-10000000000
χ492-2-2-2-2222-1-2-22211-1-1-111-222-2-1-11-1-11112-2-22000000001-13−33−3−33−3333−3−3−3−33300000000-111-10000000000
χ502-2-2-2-2222-1-2-22211-1-1-111-222-2-1-11-1-11112-2-22000000001-1−33−333−33−3−3−33333−3−300000000-111-10000000000
χ512-2-2-2-2222-1-2-22211-1-1-111-222-2-1-11-1-1111-222-2000000001-13−33−3−33−33−3−33333−3−3000000001-1-110000000000
χ522-2-2-2-2222-1-2-22211-1-1-111-222-2-1-11-1-1111-222-2000000001-1−33−333−33−333−3−3−3−333000000001-1-110000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-422222222000000000000-2-200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222-2-2-2-220000000000002200000000000000000000000000000000000000
χ55444-4-4-4-444000044-44-4-4-400000000000000000000−2i22i2000000000000−2i22i2−2i22i200000000000000000000000000
χ56444-4-4-4-444000044-44-4-4-4000000000000000000002i2−2i20000000000002i2−2i22i2−2i200000000000000000000000000
χ57444-4-4-4-44-20000-2-22-22220000000−2i32i3−2i32i3000000000−2i22i2000000000000i2−i2i2−i26−66−60000000000000000000000
χ58444-4-4-4-44-20000-2-22-22220000000−2i32i3−2i32i30000000002i2−2i2000000000000−i2i2−i2i2−66−660000000000000000000000
χ59444-4-4-4-44-20000-2-22-222200000002i3−2i32i3−2i3000000000−2i22i2000000000000i2−i2i2−i2−66−660000000000000000000000
χ60444-4-4-4-44-20000-2-22-222200000002i3−2i32i3−2i30000000002i2−2i2000000000000−i2i2−i2i26−66−60000000000000000000000
χ6144-44-44-4-444-4-444-44-4-44-40000-4440000-40000000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-24-4-44-22-222-2200002-2-2000020000000000000023−23−23230000000000000000000000000000000000
χ6344-44-44-4-4-24-4-44-22-222-2200002-2-20000200000000000000−232323−230000000000000000000000000000000000
χ6444-44-44-4-4-2-444-4-22-222-220000-2220000-20000004-40000000000-2-222000000000000000000000000000000
χ6544-44-44-4-4-2-444-4-22-222-220000-2220000-2000000-44000000000022-2-2000000000000000000000000000000
χ6644-4-44-44-4400004-4-4-44-440000000000000000000000000000000000000000000000004i−4i00000000000000
χ6744-4-44-44-4400004-4-4-44-44000000000000000000000000000000000000000000000000−4i4i00000000000000
χ684-444-4-44-440000-44-4-444-400000000000000000000000000000000000000000000004i−4i0000000000000000
χ694-444-4-44-440000-44-4-444-40000000000000000000000000000000000000000000000−4i4i0000000000000000
χ704-44-444-4-444-44-4-444-4-4-4400004-440000-40000000000000000000000000000000000000000000000000000
χ714-44-444-4-4-24-44-42-2-2222-20000-22-20000200000000000000000023−23−2323000000000000000000000000000000
χ724-44-444-4-4-24-44-42-2-2222-20000-22-200002000000000000000000−232323−23000000000000000000000000000000
χ734-44-444-4-4-2-44-442-2-2222-200002-220000-200004-400000000-2-2220000000000000000000000000000000000
χ744-44-444-4-4-2-44-442-2-2222-200002-220000-20000-440000000022-2-20000000000000000000000000000000000
χ754-4-444-4-4440000-4-4-44-444000000000000000000000022−220000000000000022−22−22220000000000000000000000
χ764-4-444-4-4440000-4-4-44-4440000000000000000000000−222200000000000000−222222−220000000000000000000000
χ774-4-444-4-44-20000222-22-2-20000000−2i32i32i3−2i30000000000022−220000000000−i6i6i6−i6−222−20000000000000000000000
χ784-4-444-4-44-20000222-22-2-20000000−2i32i32i3−2i300000000000−22220000000000i6−i6−i6i62−2−220000000000000000000000
χ794-4-444-4-44-20000222-22-2-200000002i3−2i3−2i32i30000000000022−220000000000i6−i6−i6i6−222−20000000000000000000000
χ804-4-444-4-44-20000222-22-2-200000002i3−2i3−2i32i300000000000−22220000000000−i6i6i6−i62−2−220000000000000000000000
χ814-4-4-4-4444-244-4-422-2-2-2224-44-422-2-2-222-2000000000000-2200000000000000000000000000000000000000
χ824-4-4-4-4444-244-4-422-2-2-222-44-4422-222-2-2-20000000000002-200000000000000000000000000000000000000
χ8388-8-88-88-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-888-8-88-8-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000

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