Finite Group Databasebeta

← Group #10849338

Character table — Group #10849338

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order12222222344446666666444444441212121212121212121212122244446666888812121212121212121212121224242424242424244444224444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-11-1-1-1-111
χ6111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-11111-1-1
χ7111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1-111111-1-1
χ8111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-111-1-1-1-1-111
χ911111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-111111-1-11-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111111-1-1-1-1-111-11
χ1111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1111-1-111-11
χ1211111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-111111-1-1-111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111-1-1-1111-1
χ17222222222-2-2-2-2222222222-2-20000-2-22222-2-2-2-2-2-2000000000000000000000000000000000022-2-200200-2000000
χ18222222222-2-2-2-2222222222-2-20000-2-22222-2-2-2-2-2-20000000000000000000000000000000000-2-22200-2002000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-22222-2-20000000000000000000000000000000000222200-200-2000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-2-2-2002002000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-211111111-1-1-1-1111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-222221111-2-2-2-2-1-1-1-1-1-1-1-11111111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211112222111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-2-222-2-2111122-2-2-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-2-2-2-2221111-2-2221111-1-1-1-1-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-12222-2-2-1-1-1-1-2-222-1-1-1-1111111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-122-2-222-1-1-1-122-2-21111-1-1-1-11111-1-1-1-111110000000000000000
χ2922-22-22-2-22-22-222-22-22-2-200002i2i−2i−2i2-2000000002-200002-20000002i−2i000022-2-22i2i−2i−2i00002i2i−2i−2i0000000000000000
χ3022-22-22-2-22-22-222-22-22-2-200002i2i−2i−2i2-2000000002-20000-22000000−2i2i0000-2-2222i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ3122-22-22-2-22-22-222-22-22-2-20000−2i−2i2i2i2-2000000002-200002-2000000−2i2i000022-2-2−2i−2i2i2i0000−2i−2i2i2i0000000000000000
χ3222-22-22-2-22-22-222-22-22-2-20000−2i−2i2i2i2-2000000002-20000-220000002i−2i0000-2-222−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ3322-22-22-2-2-1-22-22-11-11-11100002i2i−2i−2i-1133−3−333−3−3-1100002-2−i3−i3i3i3002i−2i33−3−3-1-111−i−iii−i3−i3i3i3−i−iii0000000000000000
χ3422-22-22-2-2-1-22-22-11-11-11100002i2i−2i−2i-1133−3−333−3−3-110000-22−i3−i3i3i300−2i2i−3−33311-1-1−i−iiii3i3−i3−i3ii−i−i0000000000000000
χ3522-22-22-2-2-1-22-22-11-11-11100002i2i−2i−2i-11−3−333−3−333-1100002-2i3i3−i3−i3002i−2i−3−333-1-111−i−iiii3i3−i3−i3−i−iii0000000000000000
χ3622-22-22-2-2-1-22-22-11-11-11100002i2i−2i−2i-11−3−333−3−333-110000-22i3i3−i3−i300−2i2i33−3−311-1-1−i−iii−i3−i3i3i3ii−i−i0000000000000000
χ3722-22-22-2-2-1-22-22-11-11-1110000−2i−2i2i2i-1133−3−333−3−3-1100002-2i3i3−i3−i300−2i2i33−3−3-1-111ii−i−ii3i3−i3−i3ii−i−i0000000000000000
χ3822-22-22-2-2-1-22-22-11-11-1110000−2i−2i2i2i-1133−3−333−3−3-110000-22i3i3−i3−i3002i−2i−3−33311-1-1ii−i−i−i3−i3i3i3−i−iii0000000000000000
χ3922-22-22-2-2-1-22-22-11-11-1110000−2i−2i2i2i-11−3−333−3−333-1100002-2−i3−i3i3i300−2i2i−3−333-1-111ii−i−i−i3−i3i3i3ii−i−i0000000000000000
χ4022-22-22-2-2-1-22-22-11-11-1110000−2i−2i2i2i-11−3−333−3−333-110000-22−i3−i3i3i3002i−2i33−3−311-1-1ii−i−ii3i3−i3−i3−i−iii0000000000000000
χ412-22-222-2-22-2-222-222-2-22-200002i−2i2i−2i2-200000000-22002-20000002i−2i002-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ422-22-222-2-22-2-222-222-2-22-200002i−2i2i−2i2-200000000-2200-22000000−2i2i00-22-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ432-22-222-2-22-2-222-222-2-22-20000−2i2i−2i2i2-200000000-22002-2000000−2i2i002-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ442-22-222-2-22-2-222-222-2-22-20000−2i2i−2i2i2-200000000-2200-220000002i−2i00-22-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ452-22-222-2-2-1-2-2221-1-111-1100002i−2i2i−2i-113−33−33−33−31-1002-200−i3i3−i3i32i−2i00-11-113−33−3−ii−ii−ii−ii−i3i3−i3i30000000000000000
χ462-22-222-2-2-1-2-2221-1-111-1100002i−2i2i−2i-113−33−33−33−31-100-2200−i3i3−i3i3−2i2i001-11-1−33−33−ii−iii−ii−ii3−i3i3−i30000000000000000
χ472-22-222-2-2-1-2-2221-1-111-1100002i−2i2i−2i-11−33−33−33−331-1002-200i3−i3i3−i32i−2i00-11-11−33−33−ii−ii−ii−iii3−i3i3−i30000000000000000
χ482-22-222-2-2-1-2-2221-1-111-1100002i−2i2i−2i-11−33−33−33−331-100-2200i3−i3i3−i3−2i2i001-11-13−33−3−ii−iii−ii−i−i3i3−i3i30000000000000000
χ492-22-222-2-2-1-2-2221-1-111-110000−2i2i−2i2i-113−33−33−33−31-1002-200i3−i3i3−i3−2i2i00-11-113−33−3i−ii−ii−ii−ii3−i3i3−i30000000000000000
χ502-22-222-2-2-1-2-2221-1-111-110000−2i2i−2i2i-113−33−33−33−31-100-2200i3−i3i3−i32i−2i001-11-1−33−33i−ii−i−ii−ii−i3i3−i3i30000000000000000
χ512-22-222-2-2-1-2-2221-1-111-110000−2i2i−2i2i-11−33−33−33−331-1002-200−i3i3−i3i3−2i2i00-11-11−33−33i−ii−ii−ii−i−i3i3−i3i30000000000000000
χ522-22-222-2-2-1-2-2221-1-111-110000−2i2i−2i2i-11−33−33−33−331-100-2200−i3i3−i3i32i−2i001-11-13−33−3i−ii−i−ii−iii3−i3i3−i30000000000000000
χ532-2-2-2-222222-2-22-2-222-2-222-22-22-2-22222-2-222-2-22-2-22-200002-2-220000000000002-2-22000000000000000000000000
χ542-2-2-2-222222-2-22-2-222-2-222-22-2-222-2222-2-222-2-22-2-2-220000-222-2000000000000-222-2000000000000000000000000
χ552-2-2-2-222222-2-22-2-222-2-22-22-222-2-2222-222-2-222-2-2-2-220000-222-20000000000002-2-22000000000000000000000000
χ562-2-2-2-222222-2-22-2-222-2-22-22-22-222-222-222-2-222-2-2-22-200002-2-22000000000000-222-2000000000000000000000000
χ572-2-2-2-22222-222-2-2-222-2-222-2-220000-2-22-2-22-222-222000000000000000000000000000000000000002-202-20000000
χ582-2-2-2-22222-222-2-2-222-2-222-2-220000-2-22-2-22-222-22200000000000000000000000000000000000000-220-220000000
χ592-2-2-2-22222-222-2-2-222-2-22-222-20000-2-2-222-22-2-2222000000000000000000000000000000000000002-20-220000000
χ602-2-2-2-22222-222-2-2-222-2-22-222-20000-2-2-222-22-2-222200000000000000000000000000000000000000-2202-20000000
χ612-2-2-2-2222-12-2-2211-1-111-12-22-22-2-22-1-1-111-1-111-1112-20000-111-100003−3−33−333−3-111-1−333−33−3−330000000000000000
χ622-2-2-2-2222-12-2-2211-1-111-12-22-22-2-22-1-1-111-1-111-1112-20000-111-10000−333−33−3−33-111-13−3−33−333−30000000000000000
χ632-2-2-2-2222-12-2-2211-1-111-12-22-2-222-2-1-1-111-1-111-111-2200001-1-1100003−3−33−333−31-1-113−3−33−333−30000000000000000
χ642-2-2-2-2222-12-2-2211-1-111-12-22-2-222-2-1-1-111-1-111-111-2200001-1-110000−333−33−3−331-1-11−333−33−3−330000000000000000
χ652-2-2-2-2222-12-2-2211-1-111-1-22-222-2-22-1-11-1-111-1-1111-2200001-1-1100003−3−333−3−33-111-1−333−3−333−30000000000000000
χ662-2-2-2-2222-12-2-2211-1-111-1-22-222-2-22-1-11-1-111-1-1111-2200001-1-110000−333−3−333−3-111-13−3−333−3−330000000000000000
χ672-2-2-2-2222-12-2-2211-1-111-1-22-22-222-2-1-11-1-111-1-11112-20000-111-100003−3−333−3−331-1-113−3−333−3−330000000000000000
χ682-2-2-2-2222-12-2-2211-1-111-1-22-22-222-2-1-11-1-111-1-11112-20000-111-10000−333−3−333−31-1-11−333−3−333−30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4000022-2-2-2-222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ71444-4-4-44-44000044-44-4-4-40000000000000000000000000000000000000000000000000000004-400000000000000
χ72444-4-4-44-44000044-44-4-4-4000000000000000000000000000000000000000000000000000000-4400000000000000
χ7344-44-44-4-444-44-44-44-44-4-400000000-4400000000-4400000000000000000000000000000000000000000000000000
χ7444-44-44-4-4-24-44-4-22-22-222000000002-22323−23−23−23−2323232-200000000000000000000000000000000000000000000000000
χ7544-44-44-4-4-24-44-4-22-22-222000000002-2−23−2323232323−23−232-200000000000000000000000000000000000000000000000000
χ7644-4-44-4-44400004-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000022−2200
χ7744-4-44-4-44400004-4-4-4-444000000000000000000000000000000000000000000000000000000000000000000−222200
χ784-444-4-4-4440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000000022−220000
χ794-444-4-4-4440000-44-4-44-440000000000000000000000000000000000000000000000000000000000000000−22220000
χ804-44-444-4-4444-4-4-444-4-44-400000000-44000000004-400000000000000000000000000000000000000000000000000
χ814-44-444-4-4-244-4-42-2-222-22000000002-223−2323−23−2323−2323-2200000000000000000000000000000000000000000000000000
χ824-44-444-4-4-244-4-42-2-222-22000000002-2−2323−232323−2323−23-2200000000000000000000000000000000000000000000000000
χ834-4-444-44-440000-4-4-4444-4000000000000000000000000000000000000000000000000000000004i−4i000000000000
χ844-4-444-44-440000-4-4-4444-400000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ854-4-4-4-4444-2-444-422-2-222-24-4-44000022-222-22-2-22-2-200000000000000000000000000000000000000000000000000
χ864-4-4-4-4444-2-444-422-2-222-2-444-40000222-2-22-222-2-2-200000000000000000000000000000000000000000000000000
χ87888-8-8-88-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-88-8-88-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-8-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-88-8-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000

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