Finite Group Databasebeta

← Group #10855134

Character table — Group #10855134

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order12222222344446666666224444446666121212121212121244444488881212121212121212121212121212121224242424242424244444244444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ911111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11-1-1-11111-1-11-1
χ1011111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1111-1-1-1-111-11
χ1111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111-11
χ1211111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-11-111-1-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-11-1-11111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-1111-1
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-2-2-2-2-200000000000000000000000000000000002222-2-20000000000
χ18222222222-2-2-2-2222222222-2-200002222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-2-2-2220000000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-22222-2000000000000000000000000000000000022-2-2-220000000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-22222-20000000000000000000000000000000000-2-2222-20000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-21111-1-1-1-1-1-1-1-11111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-11111-1-2-222-2-222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-11111-1-2-2-2-222-2-222-1-1-1-1-1-1-1-1111111111111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-11111-12222-2-2-2-22211111111-1-1-1-1-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-11111-122-2-22222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ2922-222-2-2-22-222-222-2-22-2-200002i2i−2i−2i00002-2-20000200002i−2i002-22i2i−2i−2i2i2i−2i−2i00000000000022-2-20000000000000000
χ3022-222-2-2-22-222-222-2-22-2-200002i2i−2i−2i00002-2-2000020000−2i2i00-22−2i−2i2i2i2i2i−2i−2i000000000000-2-2220000000000000000
χ3122-222-2-2-22-222-222-2-22-2-20000−2i−2i2i2i00002-2-20000200002i−2i00-222i2i−2i−2i−2i−2i2i2i000000000000-2-2220000000000000000
χ3222-222-2-2-22-222-222-2-22-2-20000−2i−2i2i2i00002-2-2000020000−2i2i002-2−2i−2i2i2i−2i−2i2i2i00000000000022-2-20000000000000000
χ3322-222-2-2-2-1-222-2-1-111-11100002i2i−2i−2i−i3−i3i3i3-111−i3−i3i3i3-100002i−2i002-2−i−iii−i−iii33−3−333−3−3−i3−i3i3i3-1-1110000000000000000
χ3422-222-2-2-2-1-222-2-1-111-11100002i2i−2i−2i−i3−i3i3i3-111−i3−i3i3i3-10000−2i2i00-22ii−i−i−i−iii33−3−3−3−333i3i3−i3−i311-1-10000000000000000
χ3522-222-2-2-2-1-222-2-1-111-11100002i2i−2i−2ii3i3−i3−i3-111i3i3−i3−i3-100002i−2i002-2−i−iii−i−iii−3−333−3−333i3i3−i3−i3-1-1110000000000000000
χ3622-222-2-2-2-1-222-2-1-111-11100002i2i−2i−2ii3i3−i3−i3-111i3i3−i3−i3-10000−2i2i00-22ii−i−i−i−iii−3−33333−3−3−i3−i3i3i311-1-10000000000000000
χ3722-222-2-2-2-1-222-2-1-111-1110000−2i−2i2i2i−i3−i3i3i3-111−i3−i3i3i3-100002i−2i00-22−i−iiiii−i−i−3−33333−3−3i3i3−i3−i311-1-10000000000000000
χ3822-222-2-2-2-1-222-2-1-111-1110000−2i−2i2i2i−i3−i3i3i3-111−i3−i3i3i3-10000−2i2i002-2ii−i−iii−i−i−3−333−3−333−i3−i3i3i3-1-1110000000000000000
χ3922-222-2-2-2-1-222-2-1-111-1110000−2i−2i2i2ii3i3−i3−i3-111i3i3−i3−i3-100002i−2i00-22−i−iiiii−i−i33−3−3−3−333−i3−i3i3i311-1-10000000000000000
χ4022-222-2-2-2-1-222-2-1-111-1110000−2i−2i2i2ii3i3−i3−i3-111i3i3−i3−i3-10000−2i2i002-2ii−i−iii−i−i33−3−333−3−3i3i3−i3−i3-1-1110000000000000000
χ412-222-2-2-22222-2-2-2-2222-2-22-22-22i−2i2i−2i2-22-2-22-22-22-222i−2i0000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ422-222-2-2-22222-2-2-2-2222-2-22-22-2−2i2i−2i2i2-22-2-22-22-22-22−2i2i000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ432-222-2-2-22222-2-2-2-2222-2-2-22-222i−2i2i−2i-22-22-22-2-22-222−2i2i0000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ442-222-2-2-22222-2-2-2-2222-2-2-22-22−2i2i−2i2i-22-22-22-2-22-2222i−2i000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ452-222-2-2-222-2-222-2-2222-2-22-2-2200002-22-22-22-22-22-200000000000000000000000000000000000000002i−2i2i−2i000000
χ462-222-2-2-222-2-222-2-2222-2-22-2-2200002-22-22-22-22-22-20000000000000000000000000000000000000000−2i2i−2i2i000000
χ472-222-2-2-222-2-222-2-2222-2-2-222-20000-22-222-222-22-2-200000000000000000000000000000000000000002i−2i−2i2i000000
χ482-222-2-2-222-2-222-2-2222-2-2-222-20000-22-222-222-22-2-20000000000000000000000000000000000000000−2i2i2i−2i000000
χ492-222-2-2-22-122-2-211-1-1-1112-22-22i−2i2i−2i-11-111-11-11-11-12i−2i000000003−33−3−ii−ii−ii−ii3−33−3−i3i3−i3i3−i3i3−i3i30000000000000000
χ502-222-2-2-22-122-2-211-1-1-1112-22-22i−2i2i−2i-11-111-11-11-11-12i−2i00000000−33−33−ii−ii−ii−ii−33−33i3−i3i3−i3i3−i3i3−i30000000000000000
χ512-222-2-2-22-122-2-211-1-1-1112-22-2−2i2i−2i2i-11-111-11-11-11-1−2i2i000000003−33−3i−ii−ii−ii−i3−33−3i3−i3i3−i3i3−i3i3−i30000000000000000
χ522-222-2-2-22-122-2-211-1-1-1112-22-2−2i2i−2i2i-11-111-11-11-11-1−2i2i00000000−33−33i−ii−ii−ii−i−33−33−i3i3−i3i3−i3i3−i3i30000000000000000
χ532-222-2-2-22-122-2-211-1-1-111-22-222i−2i2i−2i1-11-11-111-11-1-1−2i2i000000003−33−3−ii−iii−ii−i−33−33i3−i3i3−i3−i3i3−i3i30000000000000000
χ542-222-2-2-22-122-2-211-1-1-111-22-222i−2i2i−2i1-11-11-111-11-1-1−2i2i00000000−33−33−ii−iii−ii−i3−33−3−i3i3−i3i3i3−i3i3−i30000000000000000
χ552-222-2-2-22-122-2-211-1-1-111-22-22−2i2i−2i2i1-11-11-111-11-1-12i−2i000000003−33−3i−ii−i−ii−ii−33−33−i3i3−i3i3i3−i3i3−i30000000000000000
χ562-222-2-2-22-122-2-211-1-1-111-22-22−2i2i−2i2i1-11-11-111-11-1-12i−2i00000000−33−33i−ii−i−ii−ii3−33−3i3−i3i3−i3−i3i3−i3i30000000000000000
χ572-2-22-222-22-22-22-2-2-2-222200002-2-220000-2-2200002002-2002-20000002-2-2200002-2-222-2-2200000000000000000000
χ582-2-22-222-22-22-22-2-2-2-222200002-2-220000-2-220000200-2200-220000002-2-220000-222-2-222-200000000000000000000
χ592-2-22-222-22-22-22-2-2-2-22220000-222-20000-2-2200002002-200-22000000-222-200002-2-22-222-200000000000000000000
χ602-2-22-222-22-22-22-2-2-2-22220000-222-20000-2-220000200-22002-2000000-222-20000-222-22-2-2200000000000000000000
χ612-2-22-222-2-1-22-221111-1-1-100002-2-22−i3i3i3−i311-1−i3i3i3−i3-1002-2002-200−i3i3i3−i3-111-1−i3i3i3−i3-111-1-111-1−i3i3i3−i30000000000000000
χ622-2-22-222-2-1-22-221111-1-1-100002-2-22−i3i3i3−i311-1−i3i3i3−i3-100-2200-2200i3−i3−i3i3-111-1−i3i3i3−i31-1-111-1-11i3−i3−i3i30000000000000000
χ632-2-22-222-2-1-22-221111-1-1-100002-2-22i3−i3−i3i311-1i3−i3−i3i3-1002-2002-200i3−i3−i3i3-111-1i3−i3−i3i3-111-1-111-1i3−i3−i3i30000000000000000
χ642-2-22-222-2-1-22-221111-1-1-100002-2-22i3−i3−i3i311-1i3−i3−i3i3-100-2200-2200−i3i3i3−i3-111-1i3−i3−i3i31-1-111-1-11−i3i3i3−i30000000000000000
χ652-2-22-222-2-1-22-221111-1-1-10000-222-2−i3i3i3−i311-1−i3i3i3−i3-1002-200-2200−i3i3i3−i31-1-11i3−i3−i3i3-111-11-1-11i3−i3−i3i30000000000000000
χ662-2-22-222-2-1-22-221111-1-1-10000-222-2−i3i3i3−i311-1−i3i3i3−i3-100-22002-200i3−i3−i3i31-1-11i3−i3−i3i31-1-11-111-1−i3i3i3−i30000000000000000
χ672-2-22-222-2-1-22-221111-1-1-10000-222-2i3−i3−i3i311-1i3−i3−i3i3-1002-200-2200i3−i3−i3i31-1-11−i3i3i3−i3-111-11-1-11−i3i3i3−i30000000000000000
χ682-2-22-222-2-1-22-221111-1-1-10000-222-2i3−i3−i3i311-1i3−i3−i3i3-100-22002-200−i3i3i3−i31-1-11−i3i3i3−i31-1-11-111-1i3−i3−i3i30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44400002222222-2-2-2-2200000000000000000000000000000000000000000000000000
χ71444-4-44-4-4400004-44-4-4-44000000000000000000000000000000000000000000000000000000004i−4i000000000000
χ72444-4-44-4-4400004-44-4-4-4400000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ7344-444-4-4-444-4-4444-4-44-4-4000000000000-4440000-400000000000000000000000000000000000000000000000000
χ7444-444-4-4-4-24-4-44-2-222-22200000000−2i3−2i32i32i32-2-22i32i3−2i3−2i3200000000000000000000000000000000000000000000000000
χ7544-444-4-4-4-24-4-44-2-222-222000000002i32i3−2i3−2i32-2-2−2i3−2i32i32i3200000000000000000000000000000000000000000000000000
χ7644-4-4-4-444400004-4-44-44-40000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ7744-4-4-4-444400004-4-44-44-400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ784-444-4-4-44-2-4-44422-2-2-2224-4-440000-22-22-22-22-22-2200000000000000000000000000000000000000000000000000
χ794-444-4-4-44-2-4-44422-2-2-222-444-400002-22-2-22-2-22-22200000000000000000000000000000000000000000000000000
χ804-44-44-44-440000-444-4-44-40000000000000000000000000000000000000000000000000000004i−4i00000000000000
χ814-44-44-44-440000-444-4-44-4000000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ824-4-44-444-444-44-4-4-4-4-444400000000000044-40000-400000000000000000000000000000000000000000000000000
χ834-4-44-444-4-24-44-42222-2-2-200000000−2i32i32i3−2i3-2-222i3−2i3−2i32i3200000000000000000000000000000000000000000000000000
χ844-4-44-444-4-24-44-42222-2-2-2000000002i3−2i3−2i32i3-2-22−2i32i32i3−2i3200000000000000000000000000000000000000000000000000
χ854-4-4-444-4440000-44-44-4-4400000000000000000000000000000000000000000000000000000000000000000022−2200
χ864-4-4-444-4440000-44-44-4-44000000000000000000000000000000000000000000000000000000000000000000−222200
χ87888-8-88-8-8-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-8-888-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-88-88-8-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-88-400004-44-444-40000000000000000000000000000000000000000000000000000000000000000000000

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