Finite Group Databasebeta

← Group #10876094

Character table — Group #10876094

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order122222223444466666664444444412121212121212121212121244444488881212121212121212121212121212121224242424242424244444444444888844
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
χ51111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ71111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-11111-1-1
χ81111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1-1-111
χ911111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-1-1-1-1-1111-1
χ1011111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111111-1-1-11
χ1111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1111-1-1-111-1-1-11
χ1211111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1111-1-1111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-1-11111-1-11-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1111-1-1-1-111-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11-1-1-111-1-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1111-1-111-1-11-1
χ17222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000022-2-2-200200000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-222200-200000000
χ19222222222-2-2-2-22222222-2-20000222222-2-2-2-2-2-2-2-200000000000000000000000000000000002222-200-200000000
χ20222222222-2-2-2-22222222-2-20000222222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-2-2-2200200000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-21111-1-11111-1-122-2-2-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-21111-1-11111-1-1-2-2-2-222-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
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
χ2922-2-222-2-22-2-2222-2-22-22-20022-2-20000002-200002-22i−2i00002i−2i002i2i−2i−2i000022-2-200002i2i−2i−2i00000000000000000000
χ3022-2-222-2-22-2-2222-2-22-22-20022-2-20000002-200002-2−2i2i0000−2i2i00−2i−2i2i2i000022-2-20000−2i−2i2i2i00000000000000000000
χ3122-2-222-2-22-2-2222-2-22-22-200-2-2220000002-200002-22i−2i0000−2i2i002i2i−2i−2i0000-2-2220000−2i−2i2i2i00000000000000000000
χ3222-2-222-2-22-2-2222-2-22-22-200-2-2220000002-200002-2−2i2i00002i−2i00−2i−2i2i2i0000-2-22200002i2i−2i−2i00000000000000000000
χ3322-2-222-2-2-1-2-222-111-11-110022-2-20033−3−3-1133−3−3-112i−2i00002i−2i00−i−iii−i3−i3i3i3-1-11133−3−3−i−iii−i3−i3i3i30000000000000000
χ3422-2-222-2-2-1-2-222-111-11-110022-2-20033−3−3-1133−3−3-11−2i2i0000−2i2i00ii−i−ii3i3−i3−i3-1-11133−3−3ii−i−ii3i3−i3−i30000000000000000
χ3522-2-222-2-2-1-2-222-111-11-110022-2-200−3−333-11−3−333-112i−2i00002i−2i00−i−iiii3i3−i3−i3-1-111−3−333−i−iiii3i3−i3−i30000000000000000
χ3622-2-222-2-2-1-2-222-111-11-110022-2-200−3−333-11−3−333-11−2i2i0000−2i2i00ii−i−i−i3−i3i3i3-1-111−3−333ii−i−i−i3−i3i3i30000000000000000
χ3722-2-222-2-2-1-2-222-111-11-1100-2-2220033−3−3-1133−3−3-112i−2i0000−2i2i00−i−iii−i3−i3i3i311-1-1−3−333ii−i−ii3i3−i3−i30000000000000000
χ3822-2-222-2-2-1-2-222-111-11-1100-2-2220033−3−3-1133−3−3-11−2i2i00002i−2i00ii−i−ii3i3−i3−i311-1-1−3−333−i−iii−i3−i3i3i30000000000000000
χ3922-2-222-2-2-1-2-222-111-11-1100-2-22200−3−333-11−3−333-112i−2i0000−2i2i00−i−iiii3i3−i3−i311-1-133−3−3ii−i−i−i3−i3i3i30000000000000000
χ4022-2-222-2-2-1-2-222-111-11-1100-2-22200−3−333-11−3−333-11−2i2i00002i−2i00ii−i−i−i3−i3i3i311-1-133−3−3−i−iiii3i3−i3−i30000000000000000
χ412-22-2-222-222-2-22-22-2-222-22i−2i00002i−2i2i−2i2i−2i-222i−2i2i−2i2-20000000000000000000000000000000000000002-202i−2i000000
χ422-22-2-222-222-2-22-22-2-222-22i−2i00002i−2i2i−2i2i−2i-222i−2i2i−2i2-2000000000000000000000000000000000000000-220−2i2i000000
χ432-22-2-222-222-2-22-22-2-222-2−2i2i0000−2i2i−2i2i−2i2i-22−2i2i−2i2i2-20000000000000000000000000000000000000002-20−2i2i000000
χ442-22-2-222-222-2-22-22-2-222-2−2i2i0000−2i2i−2i2i−2i2i-22−2i2i−2i2i2-2000000000000000000000000000000000000000-2202i−2i000000
χ452-22-2-222-22-222-2-22-2-222-22i−2i2-22-2−2i2i−2i2i−2i2i2-22i−2i2i−2i-22002i−2i000000000000002-22-22i−2i2i−2i000000000000000000000000
χ462-22-2-222-22-222-2-22-2-222-22i−2i-22-22−2i2i−2i2i−2i2i2-22i−2i2i−2i-2200−2i2i00000000000000-22-22−2i2i−2i2i000000000000000000000000
χ472-22-2-222-22-222-2-22-2-222-2−2i2i2-22-22i−2i2i−2i2i−2i2-2−2i2i−2i2i-2200−2i2i000000000000002-22-2−2i2i−2i2i000000000000000000000000
χ482-22-2-222-22-222-2-22-2-222-2−2i2i-22-222i−2i2i−2i2i−2i2-2−2i2i−2i2i-22002i−2i00000000000000-22-222i−2i2i−2i000000000000000000000000
χ492-22-2-222-2-1-222-21-111-1-112i−2i2-22-2−2i2ii−ii−i-11−ii−ii1-1002i−2i000000−i3i3−i3i33−33−3-11-11−ii−ii−i3i3−i3i33−33−30000000000000000
χ502-22-2-222-2-1-222-21-111-1-112i−2i2-22-2−2i2ii−ii−i-11−ii−ii1-1002i−2i000000i3−i3i3−i3−33−33-11-11−ii−iii3−i3i3−i3−33−330000000000000000
χ512-22-2-222-2-1-222-21-111-1-112i−2i-22-22−2i2ii−ii−i-11−ii−ii1-100−2i2i000000−i3i3−i3i33−33−31-11-1i−ii−ii3−i3i3−i3−33−330000000000000000
χ522-22-2-222-2-1-222-21-111-1-112i−2i-22-22−2i2ii−ii−i-11−ii−ii1-100−2i2i000000i3−i3i3−i3−33−331-11-1i−ii−i−i3i3−i3i33−33−30000000000000000
χ532-22-2-222-2-1-222-21-111-1-11−2i2i2-22-22i−2i−ii−ii-11i−ii−i1-100−2i2i000000−i3i3−i3i3−33−33-11-11i−ii−i−i3i3−i3i3−33−330000000000000000
χ542-22-2-222-2-1-222-21-111-1-11−2i2i2-22-22i−2i−ii−ii-11i−ii−i1-100−2i2i000000i3−i3i3−i33−33−3-11-11i−ii−ii3−i3i3−i33−33−30000000000000000
χ552-22-2-222-2-1-222-21-111-1-11−2i2i-22-222i−2i−ii−ii-11i−ii−i1-1002i−2i000000−i3i3−i3i3−33−331-11-1−ii−iii3−i3i3−i33−33−30000000000000000
χ562-22-2-222-2-1-222-21-111-1-11−2i2i-22-222i−2i−ii−ii-11i−ii−i1-1002i−2i000000i3−i3i3−i33−33−31-11-1−ii−ii−i3i3−i3i3−33−330000000000000000
χ572-2-22-22-2222-22-2-2-22-2-222002-2-22000000220000-2-200002i−2i002i−2i00002i−2i−2i2i2-2-22000000002i−2i−2i2i0000000000000000
χ582-2-22-22-2222-22-2-2-22-2-222002-2-22000000220000-2-20000−2i2i00−2i2i0000−2i2i2i−2i2-2-2200000000−2i2i2i−2i0000000000000000
χ592-2-22-22-2222-22-2-2-22-2-22200-222-2000000220000-2-200002i−2i00−2i2i00002i−2i−2i2i-222-200000000−2i2i2i−2i0000000000000000
χ602-2-22-22-2222-22-2-2-22-2-22200-222-2000000220000-2-20000−2i2i002i−2i0000−2i2i2i−2i-222-2000000002i−2i−2i2i0000000000000000
χ612-2-22-22-22-12-22-211-111-1-1002-2-2200−i3i3i3−i3-1-1i3−i3−i3i31100002i−2i002i−2i3−3−33−iii−i-111-1i3−i3−i3i33−3−33−iii−i0000000000000000
χ622-2-22-22-22-12-22-211-111-1-1002-2-2200−i3i3i3−i3-1-1i3−i3−i3i3110000−2i2i00−2i2i−333−3i−i−ii-111-1i3−i3−i3i3−333−3i−i−ii0000000000000000
χ632-2-22-22-22-12-22-211-111-1-1002-2-2200i3−i3−i3i3-1-1−i3i3i3−i31100002i−2i002i−2i−333−3−iii−i-111-1−i3i3i3−i3−333−3−iii−i0000000000000000
χ642-2-22-22-22-12-22-211-111-1-1002-2-2200i3−i3−i3i3-1-1−i3i3i3−i3110000−2i2i00−2i2i3−3−33i−i−ii-111-1−i3i3i3−i33−3−33i−i−ii0000000000000000
χ652-2-22-22-22-12-22-211-111-1-100-222-200−i3i3i3−i3-1-1i3−i3−i3i31100002i−2i00−2i2i3−3−33−iii−i1-1-11−i3i3i3−i3−333−3i−i−ii0000000000000000
χ662-2-22-22-22-12-22-211-111-1-100-222-200−i3i3i3−i3-1-1i3−i3−i3i3110000−2i2i002i−2i−333−3i−i−ii1-1-11−i3i3i3−i33−3−33−iii−i0000000000000000
χ672-2-22-22-22-12-22-211-111-1-100-222-200i3−i3−i3i3-1-1−i3i3i3−i31100002i−2i00−2i2i−333−3−iii−i1-1-11i3−i3−i3i33−3−33i−i−ii0000000000000000
χ682-2-22-22-22-12-22-211-111-1-100-222-200i3−i3−i3i3-1-1−i3i3i3−i3110000−2i2i002i−2i3−3−33i−i−ii1-1-11i3−i3−i3i3−333−3−iii−i0000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2440000-4-4222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000044-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ71444-4-4-4-44400004-44-44-4-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ72444-4-4-4-44400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000000−22220000
χ7344-44-4-44-44000044-4-4-4-44000000000000000000000000000000000000000000000000000000004-4000000000000
χ7444-44-4-44-44000044-4-4-4-4400000000000000000000000000000000000000000000000000000000-44000000000000
χ7544-4-444-4-4444-4-44-4-44-44-4000000000000-440000-4400000000000000000000000000000000000000000000000000
χ7644-4-444-4-4-244-4-4-222-22-22000000002323−23−232-2−23−2323232-200000000000000000000000000000000000000000000000000
χ7744-4-444-4-4-244-4-4-222-22-2200000000−23−2323232-22323−23−232-200000000000000000000000000000000000000000000000000
χ784-4444-4-4-440000-4-4-444-44000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ794-4444-4-4-440000-4-4-444-440000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ804-44-4-444-4-24-4-442-222-2-224i−4i00004i−4i−2i2i−2i2i2-2−2i2i−2i2i-2200000000000000000000000000000000000000000000000000
χ814-44-4-444-4-24-4-442-222-2-22−4i4i0000−4i4i2i−2i2i−2i2-22i−2i2i−2i-2200000000000000000000000000000000000000000000000000
χ824-4-44-44-444-44-44-4-44-4-444000000000000-4-400004400000000000000000000000000000000000000000000000000
χ834-4-44-44-44-2-44-4422-222-2-200000000−2i32i32i3−2i322−2i32i32i3−2i3-2-200000000000000000000000000000000000000000000000000
χ844-4-44-44-44-2-44-4422-222-2-2000000002i3−2i3−2i32i3222i3−2i3−2i32i3-2-200000000000000000000000000000000000000000000000000
χ854-4-4-44-44440000-4444-4-4-40000000000000000000000000000000000000000000000000000004i−4i00000000000000
χ864-4-4-44-44440000-4444-4-4-4000000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ87888-8-8-8-88-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-88-8-88-8-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-8888-8-8-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-88-888-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000000000

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