Finite Group Databasebeta

← Group #10822579

Character table — Group #10822579

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222222223444444446666666666612121212121212124444444444441212121212121212121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ1211111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1311111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1411111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1511111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ1611111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200002-22-2000022-2-222-2-200000000000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000-22-220000-2-222-2-22200000000000000000000000000000000
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
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100002-22-20000-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100002-22-20000-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ252222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000-22-22000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ262222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000-22-22000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222-2-2-2-222-2-22222-2-22222222-2-2-2-2-2-2-2-2222200002-2-22000022-2-2-2-22200000000000000000000000000000000
χ2822222-2-2-2-222-2-22222-2-22222222-2-2-2-2-2-2-2-222220000-222-20000-2-22222-2-200000000000000000000000000000000
χ2922222-2-2-2-22-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-1111122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ3022222-2-2-2-22-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-1111122-2-2-2-222-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ3122222-2-2-2-22-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111-2-22222-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ3222222-2-2-2-22-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111-2-222-2-22222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ3322222-2-2-2-22-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-100002-2-220000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3422222-2-2-2-22-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-100002-2-220000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3522222-2-2-2-22-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-10000-222-2000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222-2-2-2-22-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-10000-222-2000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ372222-222-2-2-222-222-2-22-2-2-222-2-2222-2-222-2-222-2-200000000000000000000000000000000000000002-22-200000000
χ382222-222-2-2-222-222-2-22-2-2-222-2-2222-2-222-2-222-2-20000000000000000000000000000000000000000-22-2200000000
χ392222-222-2-2-22-22-2-222-22-2-222-2-2222-2-2-2-222-2-2220000000000000000000000000000000000002-22-2000000000000
χ402222-222-2-2-22-22-2-222-22-2-222-2-2222-2-2-2-222-2-222000000000000000000000000000000000000-22-22000000000000
χ412222-2-2-222-222-2-2-2222-2-2-222-2-22-2-22222-2-2-2-22200000000000000000000000000000000000000002-2-2200000000
χ422222-2-2-222-222-2-2-2222-2-2-222-2-22-2-22222-2-2-2-2220000000000000000000000000000000000000000-222-200000000
χ432222-2-2-222-22-2222-2-2-22-2-222-2-22-2-222-2-22222-2-20000000000000000000000000000000000002-2-22000000000000
χ442222-2-2-222-22-2222-2-2-22-2-222-2-22-2-222-2-22222-2-2000000000000000000000000000000000000-222-2000000000000
χ4522-2-222-22-2-22222-22-2-2-222-2-2-2-222-22-22-22-22-22-22-22-20000000000000000000000002-22-22-22-20000000000000000
χ4622-2-222-22-2-22222-22-2-2-222-2-2-2-222-22-22-22-22-22-2-22-22000000000000000000000000-22-22-22-220000000000000000
χ4722-2-222-22-2-22-2-2-22-222222-2-2-2-222-22-2-22-22-22-22000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ4822-2-222-22-2-22-2-2-22-222222-2-2-2-222-22-2-22-22-22-2200000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ4922-2-222-22-2-2-1222-22-2-2-2-1-11111-1-11-11-11-11-11-112-22-2000000003−33−33−33−33−3−333−3−33-11-11-11-110000000000000000
χ5022-2-222-22-2-2-1222-22-2-2-2-1-11111-1-11-11-11-11-11-112-22-200000000−33−33−33−33−333−3−333−3-11-11-11-110000000000000000
χ5122-2-222-22-2-2-1222-22-2-2-2-1-11111-1-11-11-11-11-11-11-22-22000000003−33−33−33−3−333−3−333−31-11-11-11-10000000000000000
χ5222-2-222-22-2-2-1222-22-2-2-2-1-11111-1-11-11-11-11-11-11-22-2200000000−33−33−33−333−3−333−3−331-11-11-11-10000000000000000
χ5322-2-222-22-2-2-1-2-2-22-2222-1-11111-1-11-111-11-11-11-1000000002i−2i2i−2i3−3−333−3−33−ii−ii−ii−ii−i3i3i3−i3−i3i3i3−i30000000000000000
χ5422-2-222-22-2-2-1-2-2-22-2222-1-11111-1-11-111-11-11-11-1000000002i−2i2i−2i−333−3−333−3−ii−ii−ii−iii3−i3−i3i3i3−i3−i3i30000000000000000
χ5522-2-222-22-2-2-1-2-2-22-2222-1-11111-1-11-111-11-11-11-100000000−2i2i−2i2i3−3−333−3−33i−ii−ii−ii−ii3−i3−i3i3i3−i3−i3i30000000000000000
χ5622-2-222-22-2-2-1-2-2-22-2222-1-11111-1-11-111-11-11-11-100000000−2i2i−2i2i−333−3−333−3i−ii−ii−ii−i−i3i3i3−i3−i3i3i3−i30000000000000000
χ5722-2-22-22-22-2222-22-22-2-222-2-2-2-22-22-222-22-2-22-222-2-220000000000000000000000002-22-2-22-220000000000000000
χ5822-2-22-22-22-2222-22-22-2-222-2-2-2-22-22-222-22-2-22-22-222-2000000000000000000000000-22-222-22-20000000000000000
χ5922-2-22-22-22-22-2-22-22-22222-2-2-2-22-22-22-22-222-22-2000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ6022-2-22-22-22-22-2-22-22-22222-2-2-2-22-22-22-22-222-22-200000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ6122-2-22-22-22-2-122-22-22-2-2-1-11111-11-11-1-11-111-11-12-2-22000000003−33−3−33−333−3−33−333−3-11-111-11-10000000000000000
χ6222-2-22-22-22-2-122-22-22-2-2-1-11111-11-11-1-11-111-11-12-2-2200000000−33−333−33−3−333−33−3−33-11-111-11-10000000000000000
χ6322-2-22-22-22-2-122-22-22-2-2-1-11111-11-11-1-11-111-11-1-222-2000000003−33−3−33−33−333−33−3−331-11-1-11-110000000000000000
χ6422-2-22-22-22-2-122-22-22-2-2-1-11111-11-11-1-11-111-11-1-222-200000000−33−333−33−33−3−33−333−31-11-1-11-110000000000000000
χ6522-2-22-22-22-2-1-2-22-22-222-1-11111-11-11-11-11-1-11-11000000002i−2i−2i2i3−3−33−333−3−ii−iii−ii−i−i3i3i3−i3i3−i3−i3i30000000000000000
χ6622-2-22-22-22-2-1-2-22-22-222-1-11111-11-11-11-11-1-11-11000000002i−2i−2i2i−333−33−3−33−ii−iii−ii−ii3−i3−i3i3−i3i3i3−i30000000000000000
χ6722-2-22-22-22-2-1-2-22-22-222-1-11111-11-11-11-11-1-11-1100000000−2i2i2i−2i3−3−33−333−3i−ii−i−ii−iii3−i3−i3i3−i3i3i3−i30000000000000000
χ6822-2-22-22-22-2-1-2-22-22-222-1-11111-11-11-11-11-1-11-1100000000−2i2i2i−2i−333−33−3−33i−ii−i−ii−ii−i3i3i3−i3i3−i3−i3i30000000000000000
χ6922-2-2-22-2-22222-22-2-22-22-2-2-2-22222-2-222-2-222-2-220000000000000000000000000000000000000000000000002i−2i2i−2i
χ7022-2-2-22-2-22222-22-2-22-22-2-2-2-22222-2-222-2-222-2-22000000000000000000000000000000000000000000000000−2i2i−2i2i
χ7122-2-2-22-2-2222-22-222-22-2-2-2-2-22222-2-22-222-2-222-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ7222-2-2-22-2-2222-22-222-22-2-2-2-2-22222-2-22-222-2-222-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ7322-2-2-2-222-2222-2-222-2-22-2-2-2-2222-222-22-2-22-222-20000000000000000000000000000000000000000000000002i−2i−2i2i
χ7422-2-2-2-222-2222-2-222-2-22-2-2-2-2222-222-22-2-22-222-2000000000000000000000000000000000000000000000000−2i2i2i−2i
χ7522-2-2-2-222-222-222-2-222-2-2-2-2-2222-222-2-222-22-2-22000000000000000000000000000000000000000000002i−2i−2i2i0000
χ7622-2-2-2-222-222-222-2-222-2-2-2-2-2222-222-2-222-22-2-2200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ774444-444-4-4-4-24-444-4-44-422-2-222-2-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ784444-444-4-4-4-2-44-4-444-4422-2-222-2-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000
χ794444-4-4-444-4-24-4-4-4444-422-2-222-222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-4-444-4-2-4444-4-4-4422-2-222-222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ8144-4-4-44-4-444-24-44-4-44-442222-2-2-2-222-2-222-2-222-20000000000000000000000000000000000000000000000000000
χ8244-4-4-44-4-444-2-44-444-44-42222-2-2-2-222-22-2-222-2-220000000000000000000000000000000000000000000000000000
χ8344-4-4-4-444-44-24-4-444-4-442222-2-2-22-2-22-222-22-2-220000000000000000000000000000000000000000000000000000
χ8444-4-4-4-444-44-2-444-4-444-42222-2-2-22-2-222-2-22-222-20000000000000000000000000000000000000000000000000000
χ858-88-8000000800000000008-800-80000000000000000000000000000000000000000000000000000000000000000
χ868-88-8000000-400000000−4i34i3-44−4i34i340000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-4000000004i3−4i3-444i3−4i340000000000000000000000000000000000000000000000000000000000000000
χ888-8-8800000080000000000-8800-80000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-400000000−4i34i34-44i3−4i340000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-4000000004i3−4i34-4−4i34i340000000000000000000000000000000000000000000000000000000000000000

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