Finite Group Databasebeta

← Group #10868294

Character table — Group #10868294

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order122222223444466666664444444412121212121212121212121244444488881212121212121212121212121212121224242424242424244444244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-1-11
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-111-1-1111-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-1111-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-1-1-11111-1-1-11
χ911111111111111111111-1-1-1-1111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ1111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ1211111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-11-1-11111-1-11-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111-111-1-1-1-111-11
χ17222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000022-2-22-20000000000
χ18222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-222-220000000000
χ19222222222-2-2-2-222222220000-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000000002222-2-20000000000
χ20222222222-2-2-2-222222220000-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-2-2-2220000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-21111-1-11111-1-122-2-2-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-21111-1-11111-1-1-2-2-2-222-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111-1-12222-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111-1-1-2-2222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ2922-222-2-2-22-2-2222-2-22-22-22i2i−2i−2i000000002-200002-200002i−2i002-200002i2i−2i−2i2i2i−2i−2i0000000022-2-20000000000000000
χ3022-222-2-2-22-2-2222-2-22-22-22i2i−2i−2i000000002-200002-20000−2i2i00-220000−2i−2i2i2i2i2i−2i−2i00000000-2-2220000000000000000
χ3122-222-2-2-22-2-2222-2-22-22-2−2i−2i2i2i000000002-200002-200002i−2i00-2200002i2i−2i−2i−2i−2i2i2i00000000-2-2220000000000000000
χ3222-222-2-2-22-2-2222-2-22-22-2−2i−2i2i2i000000002-200002-20000−2i2i002-20000−2i−2i2i2i−2i−2i2i2i0000000022-2-20000000000000000
χ3322-222-2-2-2-1-2-222-111-11-112i2i−2i−2i000033−3−3-1133−3−3-1100002i−2i002-2−i3−i3i3i3−i−iii−i−iii−i3−i3i3i333−3−3-1-1110000000000000000
χ3422-222-2-2-2-1-2-222-111-11-112i2i−2i−2i000033−3−3-1133−3−3-110000−2i2i00-22i3i3−i3−i3ii−i−i−i−iii−i3−i3i3i3−3−33311-1-10000000000000000
χ3522-222-2-2-2-1-2-222-111-11-112i2i−2i−2i0000−3−333-11−3−333-1100002i−2i002-2i3i3−i3−i3−i−iii−i−iiii3i3−i3−i3−3−333-1-1110000000000000000
χ3622-222-2-2-2-1-2-222-111-11-112i2i−2i−2i0000−3−333-11−3−333-110000−2i2i00-22−i3−i3i3i3ii−i−i−i−iiii3i3−i3−i333−3−311-1-10000000000000000
χ3722-222-2-2-2-1-2-222-111-11-11−2i−2i2i2i000033−3−3-1133−3−3-1100002i−2i00-22−i3−i3i3i3−i−iiiii−i−ii3i3−i3−i3−3−33311-1-10000000000000000
χ3822-222-2-2-2-1-2-222-111-11-11−2i−2i2i2i000033−3−3-1133−3−3-110000−2i2i002-2i3i3−i3−i3ii−i−iii−i−ii3i3−i3−i333−3−3-1-1110000000000000000
χ3922-222-2-2-2-1-2-222-111-11-11−2i−2i2i2i0000−3−333-11−3−333-1100002i−2i00-22i3i3−i3−i3−i−iiiii−i−i−i3−i3i3i333−3−311-1-10000000000000000
χ4022-222-2-2-2-1-2-222-111-11-11−2i−2i2i2i0000−3−333-11−3−333-110000−2i2i002-2−i3−i3i3i3ii−i−iii−i−i−i3−i3i3i3−3−333-1-1110000000000000000
χ412-22-22-2-2222-22-2-2-22-2-2222-22-200000000220000-2-22i−2i00002i−2i002i−2i2i−2i00002-22-200002i−2i2i−2i00000000000000000000
χ422-22-22-2-2222-22-2-2-22-2-2222-22-200000000220000-2-2−2i2i0000−2i2i00−2i2i−2i2i00002-22-20000−2i2i−2i2i00000000000000000000
χ432-22-22-2-2222-22-2-2-22-2-222-22-2200000000220000-2-22i−2i0000−2i2i002i−2i2i−2i0000-22-220000−2i2i−2i2i00000000000000000000
χ442-22-22-2-2222-22-2-2-22-2-222-22-2200000000220000-2-2−2i2i00002i−2i00−2i2i−2i2i0000-22-2200002i−2i2i−2i00000000000000000000
χ452-22-22-2-22-12-22-211-111-1-12-22-20000−i3i3−i3i3-1-1−i3i3−i3i3112i−2i00002i−2i00−ii−ii3−33−3-11-11−i3i3−i3i3−ii−ii3−33−30000000000000000
χ462-22-22-2-22-12-22-211-111-1-12-22-20000−i3i3−i3i3-1-1−i3i3−i3i311−2i2i0000−2i2i00i−ii−i−33−33-11-11−i3i3−i3i3i−ii−i−33−330000000000000000
χ472-22-22-2-22-12-22-211-111-1-12-22-20000i3−i3i3−i3-1-1i3−i3i3−i3112i−2i00002i−2i00−ii−ii−33−33-11-11i3−i3i3−i3−ii−ii−33−330000000000000000
χ482-22-22-2-22-12-22-211-111-1-12-22-20000i3−i3i3−i3-1-1i3−i3i3−i311−2i2i0000−2i2i00i−ii−i3−33−3-11-11i3−i3i3−i3i−ii−i3−33−30000000000000000
χ492-22-22-2-22-12-22-211-111-1-1-22-220000−i3i3−i3i3-1-1−i3i3−i3i3112i−2i0000−2i2i00−ii−ii3−33−31-11-1i3−i3i3−i3i−ii−i−33−330000000000000000
χ502-22-22-2-22-12-22-211-111-1-1-22-220000−i3i3−i3i3-1-1−i3i3−i3i311−2i2i00002i−2i00i−ii−i−33−331-11-1i3−i3i3−i3−ii−ii3−33−30000000000000000
χ512-22-22-2-22-12-22-211-111-1-1-22-220000i3−i3i3−i3-1-1i3−i3i3−i3112i−2i0000−2i2i00−ii−ii−33−331-11-1−i3i3−i3i3i−ii−i3−33−30000000000000000
χ522-22-22-2-22-12-22-211-111-1-1-22-220000i3−i3i3−i3-1-1i3−i3i3−i311−2i2i00002i−2i00i−ii−i3−33−31-11-1−i3i3−i3i3−ii−ii−33−330000000000000000
χ532-2-2-2222-222-2-22-22-2-222-200002i−2i2i−2i2i−2i−2i2i-22−2i2i2i−2i2-200000000000000000000000000000000000000002-22i−2i000000
χ542-2-2-2222-222-2-22-22-2-222-200002i−2i2i−2i2i−2i−2i2i-22−2i2i2i−2i2-20000000000000000000000000000000000000000-22−2i2i000000
χ552-2-2-2222-222-2-22-22-2-222-20000−2i2i−2i2i−2i2i2i−2i-222i−2i−2i2i2-200000000000000000000000000000000000000002-2−2i2i000000
χ562-2-2-2222-222-2-22-22-2-222-20000−2i2i−2i2i−2i2i2i−2i-222i−2i−2i2i2-20000000000000000000000000000000000000000-222i−2i000000
χ572-2-2-2222-22-222-2-22-2-222-22i−2i−2i2i2i−2i−2i2i−2i2i2i−2i2-2−2i2i2i−2i-22002-2000000000000002i−2i−2i2i-222-2000000000000000000000000
χ582-2-2-2222-22-222-2-22-2-222-22i−2i−2i2i−2i2i2i−2i2i−2i−2i2i2-22i−2i−2i2i-2200-22000000000000002i−2i−2i2i2-2-22000000000000000000000000
χ592-2-2-2222-22-222-2-22-2-222-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2-2−2i2i2i−2i-2200-2200000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ602-2-2-2222-22-222-2-22-2-222-2−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2-22i−2i−2i2i-22002-200000000000000−2i2i2i−2i-222-2000000000000000000000000
χ612-2-2-2222-2-1-222-21-111-1-112i−2i−2i2i2i−2i−2i2ii−i−ii-11i−i−ii1-1002-20000003−3−33−i3i3i3−i3−iii−i1-1-11i3−i3−i3i3−333−30000000000000000
χ622-2-2-2222-2-1-222-21-111-1-112i−2i−2i2i2i−2i−2i2ii−i−ii-11i−i−ii1-1002-2000000−333−3i3−i3−i3i3−iii−i1-1-11−i3i3i3−i33−3−330000000000000000
χ632-2-2-2222-2-1-222-21-111-1-112i−2i−2i2i−2i2i2i−2i−iii−i-11−iii−i1-100-220000003−3−33i3−i3−i3i3−iii−i-111-1i3−i3−i3i33−3−330000000000000000
χ642-2-2-2222-2-1-222-21-111-1-112i−2i−2i2i−2i2i2i−2i−iii−i-11−iii−i1-100-22000000−333−3−i3i3i3−i3−iii−i-111-1−i3i3i3−i3−333−30000000000000000
χ652-2-2-2222-2-1-222-21-111-1-11−2i2i2i−2i2i−2i−2i2ii−i−ii-11i−i−ii1-100-220000003−3−33−i3i3i3−i3i−i−ii-111-1−i3i3i3−i33−3−330000000000000000
χ662-2-2-2222-2-1-222-21-111-1-11−2i2i2i−2i2i−2i−2i2ii−i−ii-11i−i−ii1-100-22000000−333−3i3−i3−i3i3i−i−ii-111-1i3−i3−i3i3−333−30000000000000000
χ672-2-2-2222-2-1-222-21-111-1-11−2i2i2i−2i−2i2i2i−2i−iii−i-11−iii−i1-1002-20000003−3−33i3−i3−i3i3i−i−ii1-1-11−i3i3i3−i3−333−30000000000000000
χ682-2-2-2222-2-1-222-21-111-1-11−2i2i2i−2i−2i2i2i−2i−iii−i-11−iii−i1-1002-2000000−333−3−i3i3i3−i3i−i−ii1-1-11i3−i3−i3i33−3−330000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-4222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-444-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ71444-4-44-4-44000044-4-4-4-440000000000000000000000000000000000000000000000000000004-400000000000000
χ72444-4-44-4-44000044-4-4-4-44000000000000000000000000000000000000000000000000000000-4400000000000000
χ7344-444-4-4-4444-4-44-4-44-44-4000000000000-440000-4400000000000000000000000000000000000000000000000000
χ7444-444-4-4-4-244-4-4-222-22-22000000002323−23−232-2−23−2323232-200000000000000000000000000000000000000000000000000
χ7544-444-4-4-4-244-4-4-222-22-2200000000−23−2323232-22323−23−232-200000000000000000000000000000000000000000000000000
χ7644-4-4-4-444400004-44-44-4-4000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7744-4-4-4-444400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ784-444-4-44-440000-4-4-444-440000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ794-444-4-44-440000-4-4-444-4400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ804-44-44-4-444-44-44-4-44-4-444000000000000-4-400004400000000000000000000000000000000000000000000000000
χ814-44-44-4-44-2-44-4422-222-2-200000000−2i32i3−2i32i3222i3−2i32i3−2i3-2-200000000000000000000000000000000000000000000000000
χ824-44-44-4-44-2-44-4422-222-2-2000000002i3−2i32i3−2i322−2i32i3−2i32i3-2-200000000000000000000000000000000000000000000000000
χ834-4-44-44-4440000-4444-4-4-4000000000000000000000000000000000000000000000000000000004i−4i000000000000
χ844-4-44-44-4440000-4444-4-4-400000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ854-4-4-4444-4-24-4-442-222-2-2200004i−4i4i−4i−2i2i2i−2i2-22i−2i−2i2i-2200000000000000000000000000000000000000000000000000
χ864-4-4-4444-4-24-4-442-222-2-220000−4i4i−4i4i2i−2i−2i2i2-2−2i2i2i−2i-2200000000000000000000000000000000000000000000000000
χ87888-8-88-8-8-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-8-888-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-8-88-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-88-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000000000

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