Finite Group Databasebeta

← Group #10823310

Character table — Group #10823310

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222222223444444446666666666612121212121212124444444488881212121212121212121212121212121224242424242424244444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1111-1-1-11-111-1-111-1-1
χ1011111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-11-1-111-1-111
χ1111111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111-11-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-1-11-1-1-111-1-111
χ1211111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111-11-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1111-1-111-1-1
χ1311111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-11-11-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-11-1-1-1111-1-1-1-111
χ1411111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-11-11-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11-1111-1-1-11111-1-1
χ1511111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-11-11-11-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-111-11-1-1-11-1-11111-1-1
χ1611111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-11-11-11-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11-1111-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000002-2002-20000000000
χ1822222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000-2200-220000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2322222-2-2-2-222-2-22222-2-2-2-2-2-222222-2-2-2-2-22222-20000000000000000000000000000000000002-200-220000000000
χ2422222-2-2-2-222-2-22222-2-2-2-2-2-222222-2-2-2-2-22222-2000000000000000000000000000000000000-22002-20000000000
χ2522222-2-2-2-22-122-2-2-2-2221111-1-1-1-1-111-1-1-11111-12-22-222-2-222-2-2-1-111-1-111-1-1-1-11111-1-1-1-111110000000000000000
χ2622222-2-2-2-22-122-2-2-2-2221111-1-1-1-1-111-1-1-11111-12-22-2-2-222-2-222-1-111-1-1111111-1-1-1-11111-1-1-1-10000000000000000
χ2722222-2-2-2-22-122-2-2-2-2221111-1-1-1-1-111-1-1-11111-1-22-2222-2-2-2-22211-1-111-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2822222-2-2-2-22-122-2-2-2-2221111-1-1-1-1-111-1-1-11111-1-22-22-2-22222-2-211-1-111-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ292222-222-2-2-222-222-2-22-22222222-2-2-2-22-2-222-2-2222-2-2000000002222-2-2-2-200000000000000000000000000000000
χ302222-222-2-2-222-222-2-22-22222222-2-2-2-22-2-222-2-22-2-22200000000-2-2-2-2222200000000000000000000000000000000
χ312222-222-2-2-22-22-2-222-222222222-2-2-2-2-222-2-222-2000000000000000000000000000000000000002-200-2200000000
χ322222-222-2-2-22-22-2-222-222222222-2-2-2-2-222-2-222-200000000000000000000000000000000000000-22002-200000000
χ332222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-11111-111-1-111-122-2-200000000-1-1-1-11111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ342222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-11111-111-1-111-122-2-200000000-1-1-1-11111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ352222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-11111-111-1-111-1-2-222000000001111-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ362222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-11111-111-1-111-1-2-222000000001111-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ372222-2-2-222-222-2-2-2222-2-2-2-2-2222-2-2222-2-2-2-22222-2-220000000022-2-2-2-22200000000000000000000000000000000
χ382222-2-2-222-222-2-2-2222-2-2-2-2-2222-2-2222-2-2-2-2222-222-200000000-2-22222-2-200000000000000000000000000000000
χ392222-2-2-222-22-2222-2-2-22-2-2-2-2222-2-222-22222-2-2-2000000000000000000000000000000000000002200-2-200000000
χ402222-2-2-222-22-2222-2-2-22-2-2-2-2222-2-222-22222-2-2-200000000000000000000000000000000000000-2-2002200000000
χ412222-2-2-222-2-12-2-2-2222-21111-1-1-111-1-1-11111-1-1-12-2-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ422222-2-2-222-2-12-2-2-2222-21111-1-1-111-1-1-11111-1-1-12-2-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ432222-2-2-222-2-12-2-2-2222-21111-1-1-111-1-1-11111-1-1-1-222-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ442222-2-2-222-2-12-2-2-2222-21111-1-1-111-1-1-11111-1-1-1-222-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ4522-2-222-22-2-222-22-22-2-2222-2-22-2-22-22-222-22-22-2-20000000000000000000000000000000000000000000000002-22-2
χ4622-2-222-22-2-222-22-22-2-2222-2-22-2-22-22-222-22-22-2-2000000000000000000000000000000000000000000000000-22-22
χ4722-2-222-22-2-22-22-22-222-222-2-22-2-22-22-2-2-22-22-222000000002-22-200000000000000002-22-22-22-20000000000000000
χ4822-2-222-22-2-22-22-22-222-222-2-22-2-22-22-2-2-22-22-22200000000-22-220000000000000000-22-22-22-220000000000000000
χ4922-2-222-22-2-2-1-22-22-222-2-1-111-111-11-1111-11-11-1-1000000002-22-23−33−33−33−33−33−33−33−3-11-11-11-110000000000000000
χ5022-2-222-22-2-2-1-22-22-222-2-1-111-111-11-1111-11-11-1-1000000002-22-2−33−33−33−33−33−33−33−33-11-11-11-110000000000000000
χ5122-2-222-22-2-2-1-22-22-222-2-1-111-111-11-1111-11-11-1-100000000-22-223−33−33−33−3−33−33−33−331-11-11-11-10000000000000000
χ5222-2-222-22-2-2-1-22-22-222-2-1-111-111-11-1111-11-11-1-100000000-22-22−33−33−33−333−33−33−33−31-11-11-11-10000000000000000
χ5322-2-22-22-22-222-2-22-22-22-2-2222-2-22-2-2222-2-22-22-20000000000000000000000000000000000000000000000002-2-22
χ5422-2-22-22-22-222-2-22-22-22-2-2222-2-22-2-2222-2-22-22-2000000000000000000000000000000000000000000000000-222-2
χ5522-2-22-22-22-22-222-22-22-2-2-2222-2-22-2-22-2-222-22-22000000002-2-2200000000000000002-22-2-22-220000000000000000
χ5622-2-22-22-22-22-222-22-22-2-2-2222-2-22-2-22-2-222-22-2200000000-222-20000000000000000-22-222-22-20000000000000000
χ5722-2-22-22-22-2-1-222-22-22-211-1-1-111-111-111-1-11-11-1000000002-2-223−3−333−3−333−33−3−33−33-11-111-11-10000000000000000
χ5822-2-22-22-22-2-1-222-22-22-211-1-1-111-111-111-1-11-11-1000000002-2-22−333−3−333−3−33−333−33−3-11-111-11-10000000000000000
χ5922-2-22-22-22-2-1-222-22-22-211-1-1-111-111-111-1-11-11-100000000-222-23−3−333−3−33−33−333−33−31-11-1-11-110000000000000000
χ6022-2-22-22-22-2-1-222-22-22-211-1-1-111-111-111-1-11-11-100000000-222-2−333−3−333−33−33−3−33−331-11-1-11-110000000000000000
χ6122-2-2-22-2-2222222-2-22-2-222-2-22-2-2-22-222-222-2-22-2000000000000000000000000000000000000000000002-22-20000
χ6222-2-2-22-2-2222222-2-22-2-222-2-22-2-2-22-222-222-2-22-200000000000000000000000000000000000000000000-22-220000
χ6322-2-2-22-2-2222-2-2-222-22222-2-22-2-2-22-22-22-2-222-2200002i−2i2i−2i0000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ6422-2-2-22-2-2222-2-2-222-22222-2-22-2-2-22-22-22-2-222-220000−2i2i−2i2i000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ6522-2-2-22-2-222-1-2-2-222-222-1-111-1111-11-11-111-1-11-100002i−2i2i−2i00003−33−3−33−33−iii−i−iii−i−i3i3i3−i3−i3i3i3−i30000000000000000
χ6622-2-2-22-2-222-1-2-2-222-222-1-111-1111-11-11-111-1-11-100002i−2i2i−2i0000−33−333−33−3−iii−i−iii−ii3−i3−i3i3i3−i3−i3i30000000000000000
χ6722-2-2-22-2-222-1-2-2-222-222-1-111-1111-11-11-111-1-11-10000−2i2i−2i2i00003−33−3−33−33i−i−iii−i−iii3−i3−i3i3i3−i3−i3i30000000000000000
χ6822-2-2-22-2-222-1-2-2-222-222-1-111-1111-11-11-111-1-11-10000−2i2i−2i2i0000−33−333−33−3i−i−iii−i−ii−i3i3i3−i3−i3i3i3−i30000000000000000
χ6922-2-2-2-222-22222-222-2-2-2-2-2222-2-2-222-22-22-222-2-2000000000000000000000000000000000000000000002-2-220000
χ7022-2-2-2-222-22222-222-2-2-2-2-2222-2-2-222-22-22-222-2-200000000000000000000000000000000000000000000-222-20000
χ7122-2-2-2-222-222-2-22-2-2222-2-2222-2-2-222-2-22-22-2-22200002i−2i−2i2i0000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ7222-2-2-2-222-222-2-22-2-2222-2-2222-2-2-222-2-22-22-2-2220000−2i2i2i−2i000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ7322-2-2-2-222-22-1-2-22-2-222211-1-1-1111-1-111-11-111-1-100002i−2i−2i2i00003−3−33−333−3−iii−ii−i−ii−i3i3i3−i3i3−i3−i3i30000000000000000
χ7422-2-2-2-222-22-1-2-22-2-222211-1-1-1111-1-111-11-111-1-100002i−2i−2i2i0000−333−33−3−33−iii−ii−i−iii3−i3−i3i3−i3i3i3−i30000000000000000
χ7522-2-2-2-222-22-1-2-22-2-222211-1-1-1111-1-111-11-111-1-10000−2i2i2i−2i00003−3−33−333−3i−i−ii−iii−ii3−i3−i3i3−i3i3i3−i30000000000000000
χ7622-2-2-2-222-22-1-2-22-2-222211-1-1-1111-1-111-11-111-1-10000−2i2i2i−2i0000−333−33−3−33i−i−ii−iii−i−i3i3i3−i3i3−i3−i3i30000000000000000
χ774444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000
χ7844444-4-4-4-44-2-4-44444-4-42222-2-2-2-2-222222-2-2-2-220000000000000000000000000000000000000000000000000000
χ794444-444-4-4-4-2-44-4-444-44-2-2-2-2-2-2-222222-2-222-2-220000000000000000000000000000000000000000000000000000
χ804444-4-4-444-4-2-4444-4-4-442222-2-2-222-2-22-2-2-2-22220000000000000000000000000000000000000000000000000000
χ8144-4-444-44-4-4-24-44-44-4-44-2-222-222-22-22-2-22-22-2220000000000000000000000000000000000000000000000000000
χ8244-4-44-44-44-4-24-4-44-44-4422-2-2-222-222-2-2-222-22-220000000000000000000000000000000000000000000000000000
χ8344-4-4-44-4-444-2444-4-44-4-4-2-222-2222-22-2-22-2-222-220000000000000000000000000000000000000000000000000000
χ8444-4-4-4-444-44-244-444-4-4-422-2-2-2222-2-22-22-22-2-2220000000000000000000000000000000000000000000000000000
χ858-88-80000008000000000000-88-80000000000000000000000000000000000000000000000000000000000000000
χ868-88-8000000-400000000−4i34i3−4i34i34-440000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-4000000004i3−4i34i3−4i34-440000000000000000000000000000000000000000000000000000000000000000
χ888-8-880000008000000000000-8-880000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-400000000−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-4000000004i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000000

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