Finite Group Databasebeta

← Group #10868014

Character table — Group #10868014

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212122224444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111
χ5111111111111111111111111-1-11111111-1-1-1-111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-111-1-111-111-1-1-1-1-1
χ6111111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11-1-111111
χ7111111111111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-11111-1-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-111-1-111111-1-1-1
χ911111111111111111111-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1
χ1311111111111111111111-1-1-1-1-1-11111111-1-1-1-111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11-1-11111111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-1-1-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-111-1-1111-1-1-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-2-22222-22222-2000000-2-2000000000000000022-2-200000000000-20000000
χ18222222222-2-2-2-222222220000220000-2-2-22222-2-2-2-2-2-2000000-2-20000000000000000-2-2220000000000020000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222222000000220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-22000000220000000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-1-11111-10000-2-2-222-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-11111-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-11111-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1-11111-10000-2222222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ2922-22-22-2-2222-2-22-22-2-2-2200000000002-2-2000022i2i−2i−2i02-2000000000022-2-200000000002i−2i000000000000002i−2i000
χ3022-22-22-2-2222-2-22-22-2-2-2200000000002-2-2000022i2i−2i−2i0-220000000000-2-22200000000002i−2i00000000000000−2i2i000
χ3122-22-22-2-2222-2-22-22-2-2-2200000000002-2-200002−2i−2i2i2i02-2000000000022-2-20000000000−2i2i00000000000000−2i2i000
χ3222-22-22-2-2222-2-22-22-2-2-2200000000002-2-200002−2i−2i2i2i0-220000000000-2-2220000000000−2i2i000000000000002i−2i000
χ3322-22-22-2-22-2-2222-22-2-2-222i2i−2i−2i000000-2220000-22i2i−2i−2i0000000002i2i−2i−2i00000000000000−2i2i0000000002-200000000
χ3422-22-22-2-22-2-2222-22-2-2-222i2i−2i−2i000000-2220000-2−2i−2i2i2i0000000002i2i−2i−2i000000000000002i−2i000000000-2200000000
χ3522-22-22-2-22-2-2222-22-2-2-22−2i−2i2i2i000000-2220000-22i2i−2i−2i000000000−2i−2i2i2i00000000000000−2i2i000000000-2200000000
χ3622-22-22-2-22-2-2222-22-2-2-22−2i−2i2i2i000000-2220000-2−2i−2i2i2i000000000−2i−2i2i2i000000000000002i−2i0000000002-200000000
χ3722-2-2-2-2222000022-22-2-2-200002-222−2−200022-2-202i−2i2i−2i000002−2000000000022−2−222−2−22i−2i00−i2−i2i2i2000000000000−i2i20
χ3822-2-2-2-2222000022-22-2-2-200002-222−2−200022-2-20−2i2i−2i2i000002−2000000000022−2−222−2−2−2i2i00i2i2−i2−i2000000000000i2−i20
χ3922-2-2-2-2222000022-22-2-2-200002-2−2−22200022-2-202i−2i2i−2i00000−220000000000−2−222−2−2222i−2i00i2i2−i2−i2000000000000i2−i20
χ4022-2-2-2-2222000022-22-2-2-200002-2−2−22200022-2-20−2i2i−2i2i00000−220000000000−2−222−2−222−2i2i00−i2−i2i2i2000000000000−i2i20
χ4122-2-2-2-2222000022-22-2-2-20000-2222−2−2000-2-22202i−2i2i−2i00000−22000000000022−2−2−2−222−2i2i00−i2−i2i2i2000000000000i2−i20
χ4222-2-2-2-2222000022-22-2-2-20000-2222−2−2000-2-2220−2i2i−2i2i00000−22000000000022−2−2−2−2222i−2i00i2i2−i2−i2000000000000−i2i20
χ4322-2-2-2-2222000022-22-2-2-20000-22−2−222000-2-22202i−2i2i−2i000002−20000000000−2−22222−2−2−2i2i00i2i2−i2−i2000000000000−i2i20
χ4422-2-2-2-2222000022-22-2-2-20000-22−2−222000-2-2220−2i2i−2i2i000002−20000000000−2−22222−2−22i−2i00−i2−i2i2i2000000000000i2−i20
χ452-222-2-22-22-222-2-2-2222-2-22i−2i2i−2i002-22-2-22-20000200000002i−2i00002i−2i2i−2i00002-22-200000000000002i−2i000000000000
χ462-222-2-22-22-222-2-2-2222-2-22i−2i2i−2i00-22-22-22-2000020000000−2i2i00002i−2i2i−2i0000-22-220000000000000−2i2i000000000000
χ472-222-2-22-22-222-2-2-2222-2-2−2i2i−2i2i002-22-2-22-2000020000000−2i2i0000−2i2i−2i2i00002-22-20000000000000−2i2i000000000000
χ482-222-2-22-22-222-2-2-2222-2-2−2i2i−2i2i00-22-22-22-20000200000002i−2i0000−2i2i−2i2i0000-22-2200000000000002i−2i000000000000
χ492-222-2-22-2-1-222-211-1-1-1112i−2i2i−2i002-22-21-11−i3i3−i3i3-100000002i−2i00−i3i3−ii−ii3−33−3-11-11−i3i3−i3i3000000000−ii3−30000000000
χ502-222-2-22-2-1-222-211-1-1-1112i−2i2i−2i002-22-21-11i3−i3i3−i3-100000002i−2i00i3−i3−ii−ii−33−33-11-11i3−i3i3−i3000000000−ii−330000000000
χ512-222-2-22-2-1-222-211-1-1-1112i−2i2i−2i00-22-221-11−i3i3−i3i3-10000000−2i2i00−i3i3−ii−ii3−33−31-11-1i3−i3i3−i3000000000i−i−330000000000
χ522-222-2-22-2-1-222-211-1-1-1112i−2i2i−2i00-22-221-11i3−i3i3−i3-10000000−2i2i00i3−i3−ii−ii−33−331-11-1−i3i3−i3i3000000000i−i3−30000000000
χ532-222-2-22-2-1-222-211-1-1-111−2i2i−2i2i002-22-21-11−i3i3−i3i3-10000000−2i2i00−i3i3i−ii−i−33−33-11-11−i3i3−i3i3000000000i−i−330000000000
χ542-222-2-22-2-1-222-211-1-1-111−2i2i−2i2i002-22-21-11i3−i3i3−i3-10000000−2i2i00i3−i3i−ii−i3−33−3-11-11i3−i3i3−i3000000000i−i3−30000000000
χ552-222-2-22-2-1-222-211-1-1-111−2i2i−2i2i00-22-221-11−i3i3−i3i3-100000002i−2i00−i3i3i−ii−i−33−331-11-1i3−i3i3−i3000000000−ii3−30000000000
χ562-222-2-22-2-1-222-211-1-1-111−2i2i−2i2i00-22-221-11i3−i3i3−i3-100000002i−2i00i3−i3i−ii−i3−33−31-11-1−i3i3−i3i3000000000−ii−330000000000
χ572-2-222-2-2222-22-2-222-2-22-22-2-2200000022-20000-200000000000002-2-2200000000000000002i−2i2i−2i000000002i−2i00000
χ582-2-222-2-2222-22-2-222-2-22-22-2-2200000022-20000-200000000000002-2-220000000000000000−2i2i−2i2i00000000−2i2i00000
χ592-2-222-2-2222-22-2-222-2-22-2-222-200000022-20000-20000000000000-222-200000000000000002i−2i2i−2i00000000−2i2i00000
χ602-2-222-2-2222-22-2-222-2-22-2-222-200000022-20000-20000000000000-222-20000000000000000−2i2i−2i2i000000002i−2i00000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000440000222-2-2-2-220000-400000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-400002222222200004000000-2-2000000000000000000000000000000000000000
χ63444-44-4-4-4400004-4-4-444-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ64444-44-4-4-4400004-4-4-444-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ6544-44-44-4-4-244-4-4-22-2222-20000000000-2220000-2000004-40000000000-2-2220000000000000000000000000000000
χ6644-44-44-4-4-244-4-4-22-2222-20000000000-2220000-200000-44000000000022-2-20000000000000000000000000000000
χ6744-44-44-4-4-2-4-444-22-2222-24i4i−4i−4i0000002-2-2000020000000000000−2i−2i2i2i00000000000000000000000000000000000
χ6844-44-44-4-4-2-4-444-22-2222-2−4i−4i4i4i0000002-2-20000200000000000002i2i−2i−2i00000000000000000000000000000000000
χ6944-4-4-4-444-20000-2-22-222200004-42222−22−22000-2-222000000000022−220000000000−2−222−2−22200000000000000000000000
χ7044-4-4-4-444-20000-2-22-222200004-4−22−222222000-2-2220000000000−2222000000000022−2−222−2−200000000000000000000000
χ7144-4-4-4-444-20000-2-22-22220000-442222−22−2200022-2-20000000000−22220000000000−2−22222−2−200000000000000000000000
χ7244-4-4-4-444-20000-2-22-22220000-44−22−22222200022-2-2000000000022−22000000000022−2−2−2−22200000000000000000000000
χ734-444-4-44-444-4-44-4-4444-4-400000000004-440000-40000000000000000000000000000000000000000000000000000
χ744-444-4-44-4-24-4-4422-2-2-2220000000000-22-2−2i32i3−2i32i32000000000002i3−2i3000000000000000000000000000000000000000
χ754-444-4-44-4-24-4-4422-2-2-2220000000000-22-22i3−2i32i3−2i3200000000000−2i32i3000000000000000000000000000000000000000
χ764-44-4-44-4440000-44-4-44-4400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ774-44-4-44-4440000-44-4-44-44000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ784-4-444-4-444-44-44-444-4-44-40000000000-4-44000040000000000000000000000000000000000000000000000000000
χ794-4-444-4-44-24-44-42-2-222-224-4-44000000-2-22000020000000000000-222-200000000000000000000000000000000000
χ804-4-444-4-44-24-44-42-2-222-22-444-4000000-2-220000200000000000002-2-2200000000000000000000000000000000000
χ814-4-444-4-44-2-44-442-2-222-22000000000022-20000-20000000000000000023−23−23230000000000000000000000000000000
χ824-4-444-4-44-2-44-442-2-222-22000000000022-20000-200000000000000000−232323−230000000000000000000000000000000
χ834-4-4-4444-440000-4-4-44-44400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ844-4-4-4444-440000-4-4-44-444000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ854-4-4-4444-4-20000222-22-2-200000022−22−2222000−2i32i32i3−2i30000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ864-4-4-4444-4-20000222-22-2-200000022−22−22220002i3−2i3−2i32i30000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ874-4-4-4444-4-20000222-22-2-2000000−222222−22000−2i32i32i3−2i300000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ884-4-4-4444-4-20000222-22-2-2000000−222222−220002i3−2i3−2i32i300000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ89888-88-8-8-8-40000-4444-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000

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