Finite Group Databasebeta

← Group #10858112

Character table — Group #10858112

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212121212121616161624242424242424244848
order12222222344446666666224412121212121212122244444466888812121212121212122424242424242424444444446612124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ611111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ911111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-11-11111-1-1-11
χ1011111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-11-1-1-1-1111-1
χ1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11-111-1-1111-1
χ1211111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111111111-1-1-11-1-111-1-1-11
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1111-1-1-1-1-111-11
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-111111-1-11-1
χ1511111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1111-1-1-111-1-11-1
χ1611111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-111-1111-1-111-11
χ17222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002200000000000000000000222200000000-2-200000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002200000000000000000000-2-2-2-2000000002200000000
χ19222222222-2-2-2-22222222-2-222-2-22222-2-200000000-2-20000000000000000000022-2-200000000-2200000000
χ20222222222-2-2-2-22222222-2-222-2-22222-2-200000000-2-200000000000000000000-2-222000000002-200000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-2-2-2-2111111111111111100000000-1-1-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000000011110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-10000000011110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-222-2-21122-2-2-1-1-1-11111-1-1-1-1111100000000-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-2-2-22211-2-2221111-1-1-1-11111-1-1-1-100000000-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-22222-2-211-2-222-1-1-1-111111111-1-1-1-10000000011-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-222-2-2221122-2-21111-1-1-1-1-1-1-1-111110000000011-1-10000000000
χ292222-2-2-2-2222-2-22-2-222-2-22-22-22222-2-2-2-22-22-200002-200000000000000000000000000002-22-20000000000
χ302222-2-2-2-2222-2-22-2-222-2-22-22-22222-2-2-2-2-22-2200002-20000000000000000000000000000-22-220000000000
χ312222-2-2-2-2222-2-22-2-222-2-2-22-2222-2-222-2-22-2-220000-2200000000000000000000000000002-2-220000000000
χ322222-2-2-2-2222-2-22-2-222-2-2-22-2222-2-222-2-2-222-20000-220000000000000000000000000000-222-20000000000
χ332222-2-2-2-22-2-2222-2-222-2-22-2-22-2-2-2-22222000000002-20000000000000000000000002i2i−2i−2i0000002i−2i000000
χ342222-2-2-2-22-2-2222-2-222-2-22-2-22-2-2-2-22222000000002-2000000000000000000000000−2i−2i2i2i000000−2i2i000000
χ352222-2-2-2-22-2-2222-2-222-2-2-222-2-2-222-2-22200000000-220000000000000000000000002i2i−2i−2i000000−2i2i000000
χ362222-2-2-2-22-2-2222-2-222-2-2-222-2-2-222-2-22200000000-22000000000000000000000000−2i−2i2i2i0000002i−2i000000
χ372222-2-2-2-2-122-2-2-111-1-1112-22-2-1-1-1-111112-22-20000-11000033−3−333−3−333−3−333−3−300000000-11-110000000000
χ382222-2-2-2-2-122-2-2-111-1-1112-22-2-1-1-1-111112-22-20000-110000−3−333−3−333−3−333−3−33300000000-11-110000000000
χ392222-2-2-2-2-122-2-2-111-1-1112-22-2-1-1-1-11111-22-220000-11000033−3−333−3−3−3−333−3−333000000001-11-10000000000
χ402222-2-2-2-2-122-2-2-111-1-1112-22-2-1-1-1-11111-22-220000-110000−3−333−3−33333−3−333−3−3000000001-11-10000000000
χ412222-2-2-2-2-122-2-2-111-1-111-22-22-1-111-1-1112-2-2200001-1000033−3−3−3−33333−3−3−3−33300000000-111-10000000000
χ422222-2-2-2-2-122-2-2-111-1-111-22-22-1-111-1-1112-2-2200001-10000−3−33333−3−3−3−33333−3−300000000-111-10000000000
χ432222-2-2-2-2-122-2-2-111-1-111-22-22-1-111-1-111-222-200001-1000033−3−3−3−333−3−33333−3−3000000001-1-110000000000
χ442222-2-2-2-2-122-2-2-111-1-111-22-22-1-111-1-111-222-200001-10000−3−33333−3−333−3−3−3−333000000001-1-110000000000
χ452-22-222-2-222-2-22-2222-2-2-200002-200002-200002i−2i000000002i−2i2i−2i00000000000000002i−2i2i−2i00000000002-200
χ462-22-222-2-222-2-22-2222-2-2-200002-200002-200002i−2i000000002i−2i2i−2i0000000000000000−2i2i−2i2i0000000000-2200
χ472-22-222-2-222-2-22-2222-2-2-200002-200002-20000−2i2i00000000−2i2i−2i2i00000000000000002i−2i2i−2i0000000000-2200
χ482-22-222-2-222-2-22-2222-2-2-200002-200002-20000−2i2i00000000−2i2i−2i2i0000000000000000−2i2i−2i2i00000000002-200
χ492-22-2-2-2222-22-22-2-2-22-2220000-2200002-20000002-200000000002-22-20000000000002-2-22000000002-20000
χ502-22-2-2-2222-22-22-2-2-22-2220000-2200002-20000002-200000000002-22-2000000000000-222-200000000-220000
χ512-22-2-2-2222-22-22-2-2-22-2220000-2200002-2000000-220000000000-22-220000000000002-2-2200000000-220000
χ522-22-2-2-2222-22-22-2-2-22-2220000-2200002-2000000-220000000000-22-22000000000000-222-2000000002-20000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-42222222200000000-2-2000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422-2-2-2-2220000000022000000000000000000000000000000000000000000
χ554444-4-4-4-4-2-4-444-222-2-2224-4-442222-2-2-2-200000000-22000000000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-444-222-2-222-444-422-2-222-2-2000000002-2000000000000000000000000000000000000000000
χ5744-4-44-4-444000044-4-4-44-40000000000000000000000−2i22i20000000000−2i22i2−2i22i200000000000000000000000000
χ5844-4-44-4-444000044-4-4-44-400000000000000000000002i2−2i200000000002i2−2i22i2−2i200000000000000000000000000
χ5944-4-44-4-44-20000-2-2222-2200000023−2323−23000000000000−2i22i20000000000i2−i2i2−i2i6−i6i6−i60000000000000000000000
χ6044-4-44-4-44-20000-2-2222-2200000023−2323−230000000000002i2−2i20000000000−i2i2−i2i2−i6i6−i6i60000000000000000000000
χ6144-4-44-4-44-20000-2-2222-22000000−2323−2323000000000000−2i22i20000000000i2−i2i2−i2−i6i6−i6i60000000000000000000000
χ6244-4-44-4-44-20000-2-2222-22000000−2323−23230000000000002i2−2i20000000000−i2i2−i2i2i6−i6i6−i60000000000000000000000
χ6344-4-4-444-4400004-44-4-4-44000000000000000000000000−2i22i2000000000000−2i22i22i2−2i20000000000000000000000
χ6444-4-4-444-4400004-44-4-4-440000000000000000000000002i2−2i20000000000002i2−2i2−2i22i20000000000000000000000
χ6544-4-4-444-4-20000-22-2222-200000023−23−232300000000000000−2i22i200000000−i6i6i6−i6i2−i2−i2i20000000000000000000000
χ6644-4-4-444-4-20000-22-2222-200000023−23−2323000000000000002i2−2i200000000i6−i6−i6i6−i2i2i2−i20000000000000000000000
χ6744-4-4-444-4-20000-22-2222-2000000−232323−2300000000000000−2i22i200000000i6−i6−i6i6i2−i2−i2i20000000000000000000000
χ6844-4-4-444-4-20000-22-2222-2000000−232323−23000000000000002i2−2i200000000−i6i6i6−i6−i2i2i2−i20000000000000000000000
χ694-44-444-4-44-444-4-4444-4-4-40000-440000-440000000000000000000000000000000000000000000000000000
χ704-44-444-4-4-24-4-442-2-2-22220000-220000-2200004i−4i00000000−2i2i−2i2i0000000000000000000000000000000000
χ714-44-444-4-4-24-4-442-2-2-22220000-220000-220000−4i4i000000002i−2i2i−2i0000000000000000000000000000000000
χ724-44-444-4-4-2-444-42-2-2-222200002-200002-200000000000000000023−23−2323000000000000000000000000000000
χ734-44-444-4-4-2-444-42-2-2-222200002-200002-2000000000000000000−232323−23000000000000000000000000000000
χ744-44-4-4-44444-44-4-4-4-44-44400004-40000-440000000000000000000000000000000000000000000000000000
χ754-44-4-4-444-24-44-4222-22-2-20000-2200002-200000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ764-44-4-4-444-24-44-4222-22-2-20000-2200002-2000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ774-44-4-4-444-2-44-44222-22-2-200002-20000-220000004-40000000000-22-22000000000000000000000000000000
χ784-44-4-4-444-2-44-44222-22-2-200002-20000-22000000-4400000000002-22-2000000000000000000000000000000
χ794-4-444-44-440000-44-4-44-44000000000000000000000000000000000000000000004i−4i000000000000000000
χ804-4-444-44-440000-44-4-44-4400000000000000000000000000000000000000000000−4i4i000000000000000000
χ814-4-44-44-4440000-4-44-444-40000000000000000000000000000000000000000004-400000000000000000000
χ824-4-44-44-4440000-4-44-444-4000000000000000000000000000000000000000000-4400000000000000000000
χ838-8-888-88-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-88-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000

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