Finite Group Databasebeta

← Group #10822445

Character table — Group #10822445

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order122222222234444444466666666666121212121212121222224444444466666666121212121212121212121212121212122222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ911111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-11-111-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-1-111
χ1111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1111-1-1-1-111
χ1211111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-1-11111-1-1
χ1311111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-11-11-1-1-111-1-111
χ1411111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-11-1111-1-111-1-1
χ1511111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-111-1-11-1-11111-1-1
χ1611111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-111-111-1-1-1-111
χ172222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ2522222-2-22-2-222222-2-2-2-22222222-2-2-2-22222-2-2-2-200002-22-200000000000022-2-222-2-2000000000000000000000000
χ2622222-2-22-2-222222-2-2-2-22222222-2-2-2-22222-2-2-2-20000-22-22000000000000-2-222-2-222000000000000000000000000
χ2722222-2-22-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-2222200002-2-2200000000000022-2-2-2-222000000000000000000000000
χ2822222-2-22-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-222220000-222-2000000000000-2-22222-2-2000000000000000000000000
χ2922222-2-22-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-1111100002-22-20000−i3−i3i3i3−i3−i3i3i3-1-111-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222-2-22-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-1111100002-22-20000i3i3−i3−i3i3i3−i3−i3-1-111-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222-2-22-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-111110000-22-220000−i3−i3i3i3−i3−i3i3i311-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ3222222-2-22-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-111110000-22-220000i3i3−i3−i3i3i3−i3−i311-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ3322222-2-22-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-100002-2-220000−i3−i3i3i3i3i3−i3−i3-1-11111-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ3422222-2-22-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-100002-2-220000i3i3−i3−i3−i3−i3i3i3-1-11111-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ3522222-2-22-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-10000-222-20000−i3−i3i3i3i3i3−i3−i311-1-1-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222-2-22-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-10000-222-20000i3i3−i3−i3−i3−i3i3i311-1-1-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ372222-22-2-22-2222-2-222-2-2-2-2222-2-222-2-222-2-222-2-2000000000000000000000000000000000000002200-2-200000000
χ382222-22-2-22-2222-2-222-2-2-2-2222-2-222-2-222-2-222-2-200000000000000000000000000000000000000-2-2002200000000
χ392222-22-2-22-22-2-222-2-222-2-2222-2-222-2-2-2-222-2-222000000000000000000000000000000000000002-200-2200000000
χ402222-22-2-22-22-2-222-2-222-2-2222-2-222-2-2-2-222-2-22200000000000000000000000000000000000000-22002-200000000
χ412222-2-22-2-22222-2-2-2-222-2-2222-2-2-2-22222-2-2-2-2220000000000000000000000000000000000002200-2-20000000000
χ422222-2-22-2-22222-2-2-2-222-2-2222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000-2-200220000000000
χ432222-2-22-2-222-2-22222-2-2-2-2222-2-2-2-222-2-22222-2-20000000000000000000000000000000000002-200-220000000000
χ442222-2-22-2-222-2-22222-2-2-2-2222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000-22002-20000000000
χ452-2-22222-2-2-222-22-22-22-2222-2-2-2-22-22-22-22-22-22-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ462-2-22222-2-2-222-22-22-22-2222-2-2-2-22-22-22-22-22-22-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ472-2-22222-2-2-22-22-22-22-22222-2-2-2-22-22-2-22-22-22-22000000002i−2i−2i2i00000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ482-2-22222-2-2-22-22-22-22-22222-2-2-2-22-22-2-22-22-22-2200000000−2i2i2i−2i0000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ492-2-22222-2-2-2-12-22-22-22-2-1-1-11111-11-11-11-11-11-11000000002i−2i2i−2i−i3i3−i3i3−i3i3−i3i33−33−33−33−3−ii−ii−ii−ii0000000000000000
χ502-2-22222-2-2-2-12-22-22-22-2-1-1-11111-11-11-11-11-11-11000000002i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−33−33−33−33−ii−ii−ii−ii0000000000000000
χ512-2-22222-2-2-2-12-22-22-22-2-1-1-11111-11-11-11-11-11-1100000000−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3−33−33−33−33i−ii−ii−ii−i0000000000000000
χ522-2-22222-2-2-2-12-22-22-22-2-1-1-11111-11-11-11-11-11-1100000000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i33−33−33−33−3i−ii−ii−ii−i0000000000000000
χ532-2-22222-2-2-2-1-22-22-22-22-1-1-11111-11-111-11-11-11-1000000002i−2i−2i2i−i3i3−i3i3i3−i3i3−i33−33−3−33−33−ii−iii−ii−i0000000000000000
χ542-2-22222-2-2-2-1-22-22-22-22-1-1-11111-11-111-11-11-11-1000000002i−2i−2i2ii3−i3i3−i3−i3i3−i3i3−33−333−33−3−ii−iii−ii−i0000000000000000
χ552-2-22222-2-2-2-1-22-22-22-22-1-1-11111-11-111-11-11-11-100000000−2i2i2i−2i−i3i3−i3i3i3−i3i3−i3−33−333−33−3i−ii−i−ii−ii0000000000000000
χ562-2-22222-2-2-2-1-22-22-22-22-1-1-11111-11-111-11-11-11-100000000−2i2i2i−2ii3−i3i3−i3−i3i3−i3i33−33−3−33−33i−ii−i−ii−ii0000000000000000
χ572-2-222-2-2-22222-22-2-22-22222-2-2-2-2-22-222-22-2-22-222-22-2000000002-2-222-2-2200000000000000000000000000000000
χ582-2-222-2-2-22222-22-2-22-22222-2-2-2-2-22-222-22-2-22-22-22-2200000000-222-2-222-200000000000000000000000000000000
χ592-2-222-2-2-2222-22-222-22-2222-2-2-2-2-22-22-22-222-22-22-2-22000000002-2-22-222-200000000000000000000000000000000
χ602-2-222-2-2-2222-22-222-22-2222-2-2-2-2-22-22-22-222-22-2-222-200000000-222-22-2-2200000000000000000000000000000000
χ612-2-222-2-2-222-12-22-2-22-22-1-1-111111-11-1-11-111-11-12-22-200000000-111-1-111-13−3−333−3−333−3−333−3−330000000000000000
χ622-2-222-2-2-222-12-22-2-22-22-1-1-111111-11-1-11-111-11-12-22-200000000-111-1-111-1−333−3−333−3−333−3−333−30000000000000000
χ632-2-222-2-2-222-12-22-2-22-22-1-1-111111-11-1-11-111-11-1-22-22000000001-1-111-1-113−3−333−3−33−333−3−333−30000000000000000
χ642-2-222-2-2-222-12-22-2-22-22-1-1-111111-11-1-11-111-11-1-22-22000000001-1-111-1-11−333−3−333−33−3−333−3−330000000000000000
χ652-2-222-2-2-222-1-22-222-22-2-1-1-111111-11-11-11-1-11-112-2-2200000000-111-11-1-113−3−33−333−33−3−33−333−30000000000000000
χ662-2-222-2-2-222-1-22-222-22-2-1-1-111111-11-11-11-1-11-112-2-2200000000-111-11-1-11−333−33−3−33−333−33−3−330000000000000000
χ672-2-222-2-2-222-1-22-222-22-2-1-1-111111-11-11-11-1-11-11-222-2000000001-1-11-111-13−3−33−333−3−333−33−3−330000000000000000
χ682-2-222-2-2-222-1-22-222-22-2-1-1-111111-11-11-11-1-11-11-222-2000000001-1-11-111-1−333−33−3−333−3−33−333−30000000000000000
χ692-2-22-22-22-2222-2-222-2-22-2-22-2-2222-2-222-2-222-2-22000000000000000000000000000000000000000000002-22-20000
χ702-2-22-22-22-2222-2-222-2-22-2-22-2-2222-2-222-2-222-2-2200000000000000000000000000000000000000000000-22-220000
χ712-2-22-22-22-222-222-2-222-2-2-22-2-2222-2-22-222-2-222-2000000000000000000000000000000000000000000002-2-220000
χ722-2-22-22-22-222-222-2-222-2-2-22-2-2222-2-22-222-2-222-200000000000000000000000000000000000000000000-222-20000
χ732-2-22-2-2222-222-2-22-222-2-2-22-2-222-222-22-2-22-222-20000000000000000000000000000000000000000000000002-22-2
χ742-2-22-2-2222-222-2-22-222-2-2-22-2-222-222-22-2-22-222-2000000000000000000000000000000000000000000000000-22-22
χ752-2-22-2-2222-22-222-22-2-22-2-22-2-222-222-2-222-22-2-220000000000000000000000000000000000000000000000002-2-22
χ762-2-22-2-2222-22-222-22-2-22-2-22-2-222-222-2-222-22-2-22000000000000000000000000000000000000000000000000-222-2
χ774444-44-4-44-4-244-4-444-4-422-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ784444-44-4-44-4-2-4-444-4-44422-2-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000
χ794444-4-44-4-44-244-4-4-4-44422-2-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-44-4-44-2-4-44444-4-422-2-2-22222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ814-4-44-44-44-44-24-4-444-4-4422-222-2-2-222-2-222-2-222-20000000000000000000000000000000000000000000000000000
χ824-4-44-44-44-44-2-444-4-444-422-222-2-2-222-22-2-222-2-220000000000000000000000000000000000000000000000000000
χ834-4-44-4-4444-4-24-4-44-444-422-222-2-22-2-22-222-22-2-220000000000000000000000000000000000000000000000000000
χ844-4-44-4-4444-4-2-444-44-4-4422-222-2-22-2-222-2-22-222-20000000000000000000000000000000000000000000000000000
χ8588-8-800000080000000000-88-8000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000−4i34i34-44−4i34i30000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-4000000004i3−4i34-444i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ888-88-800000080000000000-8-88000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000-400000000−4i34i344-44i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000-4000000004i3−4i344-4−4i34i30000000000000000000000000000000000000000000000000000000000000000

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