Finite Group Databasebeta

← Group #10876227

Character table — Group #10876227

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order1222222234444666666622444444121212121212121212121212444444444466121212121212121212121212121212121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-11111-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-11111-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-11111-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-11111-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-222222222222-2-2-2-2-2-2-2-22222-2-2-2-22-20000000022-2-222-2-200000000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-2-2-22222-220000000022-2-2-2-22200000000000000000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-222-2-2-2-22222-2-2-2-2-2200000000-2-222-2-22200000000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-222222-200000000-2-22222-2-200000000000000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-2-22222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-2-2-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-111111111-1-1-1-10000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-222111111111111-1-1-1-1-1-1-1-111110000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112222-2-2-2-2221111-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122-2-22222-2-21111-1-1-1-111111111-1-1-1-1-1-1-1-10000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-1-1-1-111112-200000000-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-1-1-1-111112-200000000-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-1-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-1-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-220000000011-1-111-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-220000000011-1-111-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-12-20000000011-1-1-1-111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-12-20000000011-1-1-1-111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3722-2-2-222-2222-2-222-2-2-2-22002i−2i2i−2i0022-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000002-2002i−2i00000000
χ3822-2-2-222-2222-2-222-2-2-2-22002i−2i2i−2i0022-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000-2200−2i2i00000000
χ3922-2-2-222-2222-2-222-2-2-2-2200−2i2i−2i2i0022-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000002-200−2i2i00000000
χ4022-2-2-222-2222-2-222-2-2-2-2200−2i2i−2i2i0022-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000-22002i−2i00000000
χ4122-2-2-222-22-2-22222-2-2-2-22002i−2i−2i2i00-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000002-2002i−2i0000000000
χ4222-2-2-222-22-2-22222-2-2-2-22002i−2i−2i2i00-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000-2200−2i2i0000000000
χ4322-2-2-222-22-2-22222-2-2-2-2200−2i2i2i−2i00-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000002-200−2i2i0000000000
χ4422-2-2-222-22-2-22222-2-2-2-2200−2i2i2i−2i00-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000-22002i−2i0000000000
χ452-222-2-22-222-22-2-2222-2-2-22-200002-22-22-2000000000000002i−2i2i−2i2-22-2000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ462-222-2-22-222-22-2-2222-2-2-22-200002-22-22-200000000000000−2i2i−2i2i2-22-200000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ472-222-2-22-222-22-2-2222-2-2-2-220000-222-22-2000000000000002i−2i−2i2i-22-2200000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ482-222-2-22-222-22-2-2222-2-2-2-220000-222-22-200000000000000−2i2i2i−2i-22-22000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ492-222-2-22-22-22-22-2222-2-2-22-20000-22-22-2200000000002i−2i2i−2i00002-2-2200002i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ502-222-2-22-22-22-22-2222-2-2-22-20000-22-22-220000000000−2i2i−2i2i00002-2-220000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ512-222-2-22-22-22-22-2222-2-2-2-2200002-2-22-2200000000002i−2i−2i2i0000-222-200002i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ522-222-2-22-22-22-22-2222-2-2-2-2200002-2-22-220000000000−2i2i2i−2i0000-222-20000−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ532-222-2-22-2-12-22-21-1-1-11112-200002-2-11-11−i3i3−i3i3−i3i3−i3i30000002i−2i2i−2i-11-11−i3i3−i3i33−3−33−ii−ii3−3−33−ii−ii0000000000000000
χ542-222-2-22-2-12-22-21-1-1-11112-200002-2-11-11−i3i3−i3i3−i3i3−i3i3000000−2i2i−2i2i-11-11−i3i3−i3i3−333−3i−ii−i−333−3i−ii−i0000000000000000
χ552-222-2-22-2-12-22-21-1-1-11112-200002-2-11-11i3−i3i3−i3i3−i3i3−i30000002i−2i2i−2i-11-11i3−i3i3−i3−333−3−ii−ii−333−3−ii−ii0000000000000000
χ562-222-2-22-2-12-22-21-1-1-11112-200002-2-11-11i3−i3i3−i3i3−i3i3−i3000000−2i2i−2i2i-11-11i3−i3i3−i33−3−33i−ii−i3−3−33i−ii−i0000000000000000
χ572-222-2-22-2-12-22-21-1-1-1111-220000-22-11-11−i3i3−i3i3−i3i3−i3i30000002i−2i−2i2i1-11-1i3−i3i3−i33−3−33i−ii−i−333−3−ii−ii0000000000000000
χ582-222-2-22-2-12-22-21-1-1-1111-220000-22-11-11−i3i3−i3i3−i3i3−i3i3000000−2i2i2i−2i1-11-1i3−i3i3−i3−333−3−ii−ii3−3−33i−ii−i0000000000000000
χ592-222-2-22-2-12-22-21-1-1-1111-220000-22-11-11i3−i3i3−i3i3−i3i3−i30000002i−2i−2i2i1-11-1−i3i3−i3i3−333−3i−ii−i3−3−33−ii−ii0000000000000000
χ602-222-2-22-2-12-22-21-1-1-1111-220000-22-11-11i3−i3i3−i3i3−i3i3−i3000000−2i2i2i−2i1-11-1−i3i3−i3i33−3−33−ii−ii−333−3i−ii−i0000000000000000
χ612-222-2-22-2-1-22-221-1-1-11112-20000-221-11-1−i3i3−i3i3i3−i3i3−i3002i−2i2i−2i0000-111-1−i3i3i3−i3−ii−ii3−3−33−ii−ii3−3−330000000000000000
χ622-222-2-22-2-1-22-221-1-1-11112-20000-221-11-1−i3i3−i3i3i3−i3i3−i300−2i2i−2i2i0000-111-1−i3i3i3−i3i−ii−i−333−3i−ii−i−333−30000000000000000
χ632-222-2-22-2-1-22-221-1-1-11112-20000-221-11-1i3−i3i3−i3−i3i3−i3i3002i−2i2i−2i0000-111-1i3−i3−i3i3−ii−ii−333−3−ii−ii−333−30000000000000000
χ642-222-2-22-2-1-22-221-1-1-11112-20000-221-11-1i3−i3i3−i3−i3i3−i3i300−2i2i−2i2i0000-111-1i3−i3−i3i3i−ii−i3−3−33i−ii−i3−3−330000000000000000
χ652-222-2-22-2-1-22-221-1-1-1111-2200002-21-11-1−i3i3−i3i3i3−i3i3−i3002i−2i−2i2i00001-1-11i3−i3−i3i3−ii−ii−333−3i−ii−i3−3−330000000000000000
χ662-222-2-22-2-1-22-221-1-1-1111-2200002-21-11-1−i3i3−i3i3i3−i3i3−i300−2i2i2i−2i00001-1-11i3−i3−i3i3i−ii−i3−3−33−ii−ii−333−30000000000000000
χ672-222-2-22-2-1-22-221-1-1-1111-2200002-21-11-1i3−i3i3−i3−i3i3−i3i3002i−2i−2i2i00001-1-11−i3i3i3−i3−ii−ii3−3−33i−ii−i−333−30000000000000000
χ682-222-2-22-2-1-22-221-1-1-1111-2200002-21-11-1i3−i3i3−i3−i3i3−i3i300−2i2i2i−2i00001-1-11−i3i3i3−i3i−ii−i−333−3−ii−ii3−3−330000000000000000
χ69444-44-4-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000022−22000000
χ70444-44-4-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000000000000000−2222000000
χ7144-44-4-4-44400004-4-44-44-4000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7244-44-4-4-44400004-4-44-44-40000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ7344-4-4-444-4-244-4-4-2-22222-2004i−4i4i−4i00-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ7444-4-4-444-4-244-4-4-2-22222-200−4i4i−4i4i00-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000
χ7544-4-4-444-4-2-4-444-2-22222-2004i−4i−4i4i0022-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000
χ7644-4-4-444-4-2-4-444-2-22222-200−4i4i4i−4i0022-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ774-44-4-44-4440000-4-44-4-444000000000000000000000000000000000000000000000000000000000000000022−220000
χ784-44-4-44-4440000-4-44-4-4440000000000000000000000000000000000000000000000000000000000000000−22220000
χ794-4-4444-4-440000-4-4-444-4400000000000000000000000000000000000000000000000000000000000000000000−2i22i2
χ804-4-4444-4-440000-4-4-444-44000000000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ814-4-4-44-44444-4-44-44-4-444-4000000004-4-440000000000000000000000000000000000000000000000000000000000
χ824-4-4-44-4444-444-4-44-4-444-400000000-444-40000000000000000000000000000000000000000000000000000000000
χ834-4-4-44-444-24-4-442-222-2-2200000000-222-223−23−232323−23−232300000000000000000000000000000000000000000000000000
χ844-4-4-44-444-24-4-442-222-2-2200000000-222-2−232323−23−232323−2300000000000000000000000000000000000000000000000000
χ854-4-4-44-444-2-444-42-222-2-22000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000000000
χ864-4-4-44-444-2-444-42-222-2-22000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000000000
χ87888-88-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-88-8-8-88-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-88-88-4000044-444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8888-8-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000

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