Finite Group Databasebeta

← Group #10702719

Character table — Group #10702719

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222222222344444444666121212126666661212121212128888888888882424242424242424242424242424242424242424242424242222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
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
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911-1-1111-1-1-1111-1-1-11-11-1-1111-1-1111-1-1-111-1-1-1111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i11-1-1
χ1011-1-1111-1-1-1111-1-1-11-11-1-1111-1-1111-1-1-111-1-1-1111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii−i−iii-1-111
χ1111-1-1111-1-1-1111-1-1-11-11-1-1111-1-1111-1-1-111-1-1-1111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii11-1-1
χ1211-1-1111-1-1-1111-1-1-11-11-1-1111-1-1111-1-1-111-1-1-1111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−iii−i−i-1-111
χ1311-1-1111-1-1-1111-1-1-11-11-1-1111-1-1111-1-1-111-1-1-11-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i−i−iii-1-111
χ1411-1-1111-1-1-1111-1-1-11-11-1-1111-1-1111-1-1-111-1-1-11-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iiiii−i−i11-1-1
χ1511-1-1111-1-1-1111-1-1-11-11-1-1111-1-1111-1-1-111-1-1-11-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1−i−iiiii−i−i-1-111
χ1611-1-1111-1-1-1111-1-1-11-11-1-1111-1-1111-1-1-111-1-1-11-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i−i−iii11-1-1
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
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
χ2322222-2-22-2-222-222-22-2-2222-2-2-2-22-2-22-2-22-222-22000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2422222-2-22-2-222-222-22-2-2222-2-2-2-22-2-22-2-22-222-2200000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2522222-2-22-2-22-22-2-22-22222222222-2-22-2-2-22-2-22-200000000000000000000000000000000000000002-22-200000000
χ2622222-2-22-2-22-22-2-22-22222222222-2-22-2-2-22-2-22-20000000000000000000000000000000000000000-22-2200000000
χ2722222-2-22-2-2-12-222-22-2-2-1-1-11111-111-111-11-1-11-1000000002i−2i2i−2i33−3−333−3−3−i−iii−i−iii−i3−i3i3i3−i3−i3i3i30000000000000000
χ2822222-2-22-2-2-12-222-22-2-2-1-1-11111-111-111-11-1-11-1000000002i−2i2i−2i−3−333−3−333−i−iii−i−iiii3i3−i3−i3i3i3−i3−i30000000000000000
χ2922222-2-22-2-2-12-222-22-2-2-1-1-11111-111-111-11-1-11-100000000−2i2i−2i2i33−3−333−3−3ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i30000000000000000
χ3022222-2-22-2-2-12-222-22-2-2-1-1-11111-111-111-11-1-11-100000000−2i2i−2i2i−3−333−3−333ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i30000000000000000
χ312222-22-2-22-222-22-22-2-22222-2-2-2-2-22-2-22-2222-22-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ322222-22-2-22-222-22-22-2-22222-2-2-2-2-22-2-22-2222-22-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ332222-22-2-22-22-22-22-222-22222222-22-2-22-2-2-2-22-2200002-22-200002-22-22-22-200000000000000000000000000000000
χ342222-22-2-22-22-22-22-222-22222222-22-2-22-2-2-2-22-220000-22-220000-22-22-22-2200000000000000000000000000000000
χ352222-22-2-22-2-1-22-22-222-2-1-1-1-1-1-1-11-111-11111-11-100002-22-20000-11-11-11-11−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ362222-22-2-22-2-1-22-22-222-2-1-1-1-1-1-1-11-111-11111-11-100002-22-20000-11-11-11-11i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ372222-22-2-22-2-1-22-22-222-2-1-1-1-1-1-1-11-111-11111-11-10000-22-2200001-11-11-11-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ382222-22-2-22-2-1-22-22-222-2-1-1-1-1-1-1-11-111-11111-11-10000-22-2200001-11-11-11-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ392222-2-22-2-222222-2-2-22-22222222-2-22-2-222-22-2-2-20000000000000000000000000000000000002-22-2000000000000
χ402222-2-22-2-222222-2-2-22-22222222-2-22-2-222-22-2-2-2000000000000000000000000000000000000-22-22000000000000
χ412222-2-22-2-222-2-2-2222-22222-2-2-2-2-2-22-2-22-22-22222-22-20000000000000000000000002-2-222-2-220000000000000000
χ422222-2-22-2-222-2-2-2222-22222-2-2-2-2-2-22-2-22-22-2222-22-22000000000000000000000000-222-2-222-20000000000000000
χ432222-2-22-2-22-1-2-2-2222-22-1-1-1111111-111-11-11-1-1-12-22-2000000003−3−333−3−333−3−333−3−33-111-1-111-10000000000000000
χ442222-2-22-2-22-1-2-2-2222-22-1-1-1111111-111-11-11-1-1-12-22-200000000−333−3−333−3−333−3−333−3-111-1-111-10000000000000000
χ452222-2-22-2-22-1-2-2-2222-22-1-1-1111111-111-11-11-1-1-1-22-22000000003−3−333−3−33−333−3−333−31-1-111-1-110000000000000000
χ462222-2-22-2-22-1-2-2-2222-22-1-1-1111111-111-11-11-1-1-1-22-2200000000−333−3−333−33−3−333−3−331-1-111-1-110000000000000000
χ4722-2-2222-2-2-22-2-2222-22-2-2-22-2-222222-2-2-2-2-2222-20000000000000000000000000000000000000000000000002i−2i−2i2i
χ4822-2-2222-2-2-22-2-2222-22-2-2-22-2-222222-2-2-2-2-2222-2000000000000000000000000000000000000000000000000−2i2i2i−2i
χ4922-2-2222-2-2-2-122-2-2-22-2211-1-1-111-1-1-1111-1-1111-122-2-22i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111110000000000000000
χ5022-2-2222-2-2-2-122-2-2-22-2211-1-1-111-1-1-1111-1-1111-122-2-2−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-111110000000000000000
χ5122-2-2222-2-2-2-122-2-2-22-2211-1-1-111-1-1-1111-1-1111-1-2-2222i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-10000000000000000
χ5222-2-2222-2-2-2-122-2-2-22-2211-1-1-111-1-1-1111-1-1111-1-2-222−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-10000000000000000
χ5322-2-22-2-2-22222-2-2-2222-2-2-22-2-2222-2-2-2222-2-2-222000000002-2-220000000022-2-2-2-222000000000000000000000000
χ5422-2-22-2-2-22222-2-2-2222-2-2-22-2-2222-2-2-2222-2-2-22200000000-222-200000000-2-22222-2-2000000000000000000000000
χ5522-2-22-2-2-2222-2222-2-2-22-2-2222-2-22-2-2-222-2222-2-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ5622-2-22-2-2-2222-2222-2-2-22-2-2222-2-22-2-2-222-2222-2-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ5722-2-22-2-2-222-12-2-2-2222-211-111-1-1-1111-1-1-1111-1-1000000002-2-22−i3−i3i3i3i3i3−i3−i3-1-11111-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ5822-2-22-2-2-222-12-2-2-2222-211-111-1-1-1111-1-1-1111-1-1000000002-2-22i3i3−i3−i3−i3−i3i3i3-1-11111-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ5922-2-22-2-2-222-12-2-2-2222-211-111-1-1-1111-1-1-1111-1-100000000-222-2−i3−i3i3i3i3i3−i3−i311-1-1-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ6022-2-22-2-2-222-12-2-2-2222-211-111-1-1-1111-1-1-1111-1-100000000-222-2i3i3−i3−i3−i3−i3i3i311-1-1-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ6122-2-2-22-22-2222-2-22-2-222-2-22-2-222-22-22-2222-22-2-2000000000000000000000000000000000000000000002-2-220000
χ6222-2-2-22-22-2222-2-22-2-222-2-22-2-222-22-22-2222-22-2-200000000000000000000000000000000000000000000-222-20000
χ6322-2-2-22-22-222-222-222-2-2-2-2222-2-2-22-22-22-2-22-22200002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6422-2-2-22-22-222-222-222-2-2-2-2222-2-2-22-22-22-2-22-2220000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6522-2-2-22-22-22-1-222-222-2-211-1-1-1111-11-11-111-11-1-100002i−2i−2i2i0000−ii−iii−ii−i3−33−3−33−33−i3i3−i3i3i3−i3i3−i30000000000000000
χ6622-2-2-22-22-22-1-222-222-2-211-1-1-1111-11-11-111-11-1-100002i−2i−2i2i0000−ii−iii−ii−i−33−333−33−3i3−i3i3−i3−i3i3−i3i30000000000000000
χ6722-2-2-22-22-22-1-222-222-2-211-1-1-1111-11-11-111-11-1-10000−2i2i2i−2i0000i−ii−i−ii−ii3−33−3−33−33i3−i3i3−i3−i3i3−i3i30000000000000000
χ6822-2-2-22-22-22-1-222-222-2-211-1-1-1111-11-11-111-11-1-10000−2i2i2i−2i0000i−ii−i−ii−ii−33−333−33−3−i3i3−i3i3i3−i3i3−i30000000000000000
χ6922-2-2-2-2222-2222-222-2-2-2-2-2222-2-2-2-2222-22-2-222-20000000000000000000000000000000000002-2-22000000000000
χ7022-2-2-2-2222-2222-222-2-2-2-2-2222-2-2-2-2222-22-2-222-2000000000000000000000000000000000000-222-2000000000000
χ7122-2-2-2-2222-22-2-22-2-2222-2-22-2-222-2-2222-2-222-2-222-2-220000000000000000000000002-2-22-222-20000000000000000
χ7222-2-2-2-2222-22-2-22-2-2222-2-22-2-222-2-2222-2-222-2-22-222-2000000000000000000000000-222-22-2-220000000000000000
χ7322-2-2-2-2222-2-1-2-22-2-222211-111-1-111-1-1-111-1-111-12-2-2200000000−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3-111-11-1-110000000000000000
χ7422-2-2-2-2222-2-1-2-22-2-222211-111-1-111-1-1-111-1-111-12-2-2200000000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3-111-11-1-110000000000000000
χ7522-2-2-2-2222-2-1-2-22-2-222211-111-1-111-1-1-111-1-111-1-222-200000000−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i31-1-11-111-10000000000000000
χ7622-2-2-2-2222-2-1-2-22-2-222211-111-1-111-1-1-111-1-111-1-222-200000000i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i31-1-11-111-10000000000000000
χ774444444444-2-4-4-4-4-4-4-4-4-2-2-22222-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000
χ7844444-4-44-4-4-2-44-4-44-444-2-2-2-2-2-2-2-222-2222-222-220000000000000000000000000000000000000000000000000000
χ794444-44-4-44-4-24-44-44-4-44-2-2-222222-222-22-2-2-22-220000000000000000000000000000000000000000000000000000
χ804444-4-44-4-44-2444-4-4-44-4-2-2-2-2-2-2-222-222-2-22-22220000000000000000000000000000000000000000000000000000
χ8144-4-4444-4-4-4-2-4-4444-44-422-222-2-2-2-2-222222-2-2-220000000000000000000000000000000000000000000000000000
χ8244-4-44-4-4-444-2-4444-4-4-4422-2-2-222-2222-2-22-2-2-2220000000000000000000000000000000000000000000000000000
χ8344-4-4-44-44-44-24-4-44-4-44422-222-2-22-22-22-2-2-22-2220000000000000000000000000000000000000000000000000000
χ8444-4-4-4-4444-4-244-444-4-4-422-2-2-22222-2-2-22-222-2-220000000000000000000000000000000000000000000000000000
χ858-88-80000008000000008-8-800000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8000000-400000000-44443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-400000000-444−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-4000000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-4000000004-44−434343−430000000000000000000000000000000000000000000000000000000000000000

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