Finite Group Databasebeta

← Group #10828186

Character table — Group #10828186

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666662222226666888812121212444422444666666668812122424242424242424224488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111111-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111
χ5111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-111-1-1-11111-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-11-1-1-1-111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-111-1-1111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-11111111-1-111111-1-111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ1211111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111111-1-111-1-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-11111111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-111-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-111-1-11-1-111-1-1-1-11
χ17222222222-2-2-2-2222222200002222220000-2-2-2-2222200-2000000000000-2-200000000-2-222000000000-2000000000
χ18222222222-2-2-2-2222222200002222220000-2-2-2-2-2-2-2-200-2000000000000-2-20000000022-2-20000000002000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-20000-2-2-2-222220020000000000002200000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-20000-2-2-2-2-2-2-2-200200000000000022000000002222000000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1000022222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-10000222-2-2-1-1-1-1-1-1-1-1-2-2-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-211112222-1-1-1-10000-2-2-222-1-1-1-11111-2-211-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-21111-2-2-2-2-1-1-1-10000-2-2-2-2-2-1-1-1-1111122111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-12222-1-1-1-10000-2-22-2-21111111122-1-1-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-10000-2-222211111111-2-2-1-111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-211112222-1-1-1-1000022-2-2-21111-1-1-1-1-2-211-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2-2-2-1-1-1-1000022-2221111-1-1-1-122111111-1-1-1-100000000-2-1-1110000000000
χ2922-22-2-22-2222-2-22-2-2-222-222-2-200000000002-22-200000000022-2-2000000000000000000002i2i−2i−2i0000002i−2i0000000
χ3022-22-2-22-2222-2-22-2-2-222-222-2-200000000002-22-200000000022-2-200000000000000000000−2i−2i2i2i000000−2i2i0000000
χ3122-22-2-22-2222-2-22-2-2-222-2-2-22200000000002-22-2000000000-2-222000000000000000000002i2i−2i−2i000000−2i2i0000000
χ3222-22-2-22-2222-2-22-2-2-222-2-2-22200000000002-22-2000000000-2-22200000000000000000000−2i−2i2i2i0000002i−2i0000000
χ3322-2-222-2-220000222-2-2-2-200002-222-2-2−i2−i2i2i200002i2i−2i−2i0000000000000−i2i200−i2−i2i2i2−i2−i2i2i2002i−2i2−22−20000000000002−20
χ3422-2-222-2-220000222-2-2-2-200002-222-2-2−i2−i2i2i20000−2i−2i2i2i0000000000000−i2i200−i2−i2i2i2−i2−i2i2i200−2i2i−22−22000000000000−220
χ3522-2-222-2-220000222-2-2-2-200002-222-2-2i2i2−i2−i200002i2i−2i−2i0000000000000i2−i200i2i2−i2−i2i2i2−i2−i2002i−2i−22−22000000000000−220
χ3622-2-222-2-220000222-2-2-2-200002-222-2-2i2i2−i2−i20000−2i−2i2i2i0000000000000i2−i200i2i2−i2−i2i2i2−i2−i200−2i2i2−22−20000000000002−20
χ3722-2-222-2-220000222-2-2-2-20000-22-2-222−i2−i2i2i200002i2i−2i−2i0000000000000i2−i200−i2−i2i2i2i2i2−i2−i200−2i2i2−22−2000000000000−220
χ3822-2-222-2-220000222-2-2-2-20000-22-2-222−i2−i2i2i20000−2i−2i2i2i0000000000000i2−i200−i2−i2i2i2i2i2−i2−i2002i−2i−22−220000000000002−20
χ3922-2-222-2-220000222-2-2-2-20000-22-2-222i2i2−i2−i200002i2i−2i−2i0000000000000−i2i200i2i2−i2−i2−i2−i2i2i200−2i2i−22−220000000000002−20
χ4022-2-222-2-220000222-2-2-2-20000-22-2-222i2i2−i2−i20000−2i−2i2i2i0000000000000−i2i200i2i2−i2−i2−i2−i2i2i2002i−2i2−22−2000000000000−220
χ412-22-22-22-222-22-2-22-222-2-22-22-20000002i−2i2i−2i22-2-200000002i−2i2-22-2000000002i−2i2i−2i00000000000002i−2i000000000000
χ422-22-22-22-222-22-2-22-222-2-22-22-2000000−2i2i−2i2i22-2-20000000−2i2i2-22-200000000−2i2i−2i2i0000000000000−2i2i000000000000
χ432-22-22-22-222-22-2-22-222-2-2-22-220000002i−2i2i−2i22-2-20000000−2i2i-22-22000000002i−2i2i−2i0000000000000−2i2i000000000000
χ442-22-22-22-222-22-2-22-222-2-2-22-22000000−2i2i−2i2i22-2-200000002i−2i-22-2200000000−2i2i−2i2i00000000000002i−2i000000000000
χ452-22-22-22-2-12-22-21-11-1-1112-22-200−i3i3−i3i32i−2i2i−2i-1-11100000002i−2i-11-11−i3−i3i3i300−i3i3−ii−ii3−33−3000000000−ii3−30000000000
χ462-22-22-22-2-12-22-21-11-1-1112-22-200−i3i3−i3i3−2i2i−2i2i-1-1110000000−2i2i-11-11−i3−i3i3i300−i3i3i−ii−i−33−33000000000i−i−330000000000
χ472-22-22-22-2-12-22-21-11-1-1112-22-200i3−i3i3−i32i−2i2i−2i-1-11100000002i−2i-11-11i3i3−i3−i300i3−i3−ii−ii−33−33000000000−ii−330000000000
χ482-22-22-22-2-12-22-21-11-1-1112-22-200i3−i3i3−i3−2i2i−2i2i-1-1110000000−2i2i-11-11i3i3−i3−i300i3−i3i−ii−i3−33−3000000000i−i3−30000000000
χ492-22-22-22-2-12-22-21-11-1-111-22-2200−i3i3−i3i32i−2i2i−2i-1-1110000000−2i2i1-11-1i3i3−i3−i300−i3i3−ii−ii3−33−3000000000i−i−330000000000
χ502-22-22-22-2-12-22-21-11-1-111-22-2200−i3i3−i3i3−2i2i−2i2i-1-11100000002i−2i1-11-1i3i3−i3−i300−i3i3i−ii−i−33−33000000000−ii3−30000000000
χ512-22-22-22-2-12-22-21-11-1-111-22-2200i3−i3i3−i32i−2i2i−2i-1-1110000000−2i2i1-11-1−i3−i3i3i300i3−i3−ii−ii−33−33000000000i−i3−30000000000
χ522-22-22-22-2-12-22-21-11-1-111-22-2200i3−i3i3−i3−2i2i−2i2i-1-11100000002i−2i1-11-1−i3−i3i3i300i3−i3i−ii−i3−33−3000000000−ii−330000000000
χ532-2-2-2-222222-2-22-2-22-22-222-2-2200000000002-2-222-22-2000002-2-2200000000000000002-2000000000000002-200000
χ542-2-2-2-222222-2-22-2-22-22-222-2-2200000000002-2-22-22-22000002-2-220000000000000000-2200000000000000-2200000
χ552-2-2-2-222222-2-22-2-22-22-22-222-200000000002-2-222-22-200000-222-200000000000000002-200000000000000-2200000
χ562-2-2-2-222222-2-22-2-22-22-22-222-200000000002-2-22-22-2200000-222-20000000000000000-22000000000000002-200000
χ572-2-2-2-22222-222-2-2-22-22-2200000000000000-222-22-22-22-200000002-22-2000000000000-2200000000000000002-2000
χ582-2-2-2-22222-222-2-2-22-22-2200000000000000-222-22-22-2-220000000-22-22000000000000-220000000000000000-22000
χ592-2-2-2-22222-222-2-2-22-22-2200000000000000-222-2-22-222-200000002-22-20000000000002-20000000000000000-22000
χ602-2-2-2-22222-222-2-2-22-22-2200000000000000-222-2-22-22-220000000-22-220000000000002-200000000000000002-2000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044-2-2-2-200002222000000-4000000000000220000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-42222000022220000004000000000000-2-20000000000000000000000000000000
χ63444-4-4-4-44400004-4-44-4-44000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ64444-4-4-4-44400004-4-44-4-440000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ6544-44-4-44-44-4-4444-4-4-444-400000000000000-44-440000000000000000000000000000000000000000000000000000
χ6644-44-4-44-4-244-4-4-2222-2-2244-4-40000000000-22-22000000000-2-222000000000000000000000000000000000000000
χ6744-44-4-44-4-244-4-4-2222-2-22-4-4440000000000-22-2200000000022-2-2000000000000000000000000000000000000000
χ6844-44-4-44-4-2-4-444-2222-2-22000000000000002-22-20000000000000−2i32i32i3−2i300000000000000000000000000000000000
χ6944-44-4-44-4-2-4-444-2222-2-22000000000000002-22-200000000000002i3−2i3−2i32i300000000000000000000000000000000000
χ7044-4-444-4-4-20000-2-2-2222200004-4-2-222−2i2−2i22i22i2000000000000000000000−2i22i200i2i2−i2−i2i2i2−i2−i200000000000000000000000
χ7144-4-444-4-4-20000-2-2-2222200004-4-2-2222i22i2−2i2−2i20000000000000000000002i2−2i200−i2−i2i2i2−i2−i2i2i200000000000000000000000
χ7244-4-444-4-4-20000-2-2-222220000-4422-2-2−2i2−2i22i22i20000000000000000000002i2−2i200i2i2−i2−i2−i2−i2i2i200000000000000000000000
χ7344-4-444-4-4-20000-2-2-222220000-4422-2-22i22i2−2i2−2i2000000000000000000000−2i22i200−i2−i2i2i2i2i2−i2−i200000000000000000000000
χ744-444-44-4-440000-4-444-44-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ754-444-44-4-440000-4-444-44-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ764-44-44-44-44-44-44-44-444-4-400000000000000-4-4440000000000000000000000000000000000000000000000000000
χ774-44-44-44-4-2-44-442-22-2-222000000−2i32i3−2i32i3000022-2-200000000000000000002i3−2i30000000000000000000000000000000
χ784-44-44-44-4-2-44-442-22-2-2220000002i3−2i32i3−2i3000022-2-20000000000000000000−2i32i30000000000000000000000000000000
χ794-4-444-4-4440000-44-4-4-444000000000022−22−2222000000000000000000000000022−22−2222000000000000000000000000000
χ804-4-444-4-4440000-44-4-4-4440000000000−222222−220000000000000000000000000−222222−22000000000000000000000000000
χ814-4-444-4-44-200002-2222-2-2000000−2i32i32i3−2i322−22−22220000000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ824-4-444-4-44-200002-2222-2-2000000−2i32i32i3−2i3−222222−2200000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ834-4-444-4-44-200002-2222-2-20000002i3−2i3−2i32i322−22−22220000000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ844-4-444-4-44-200002-2222-2-20000002i3−2i3−2i32i3−222222−2200000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ854-4-4-4-4444-24-4-4422-22-22-24-4-440000000000-222-2000000000-222-2000000000000000000000000000000000000000
χ864-4-4-4-4444-24-4-4422-22-22-2-444-40000000000-222-20000000002-2-22000000000000000000000000000000000000000
χ874-4-4-4-4444-2-444-422-22-22-2000000000000002-2-2200004-40000000-22-2200000000000000000000000000000000000
χ884-4-4-4-4444-2-444-422-22-22-2000000000000002-2-220000-4400000002-22-200000000000000000000000000000000000
χ89888-8-8-8-88-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-888-88-8-8-4000044-4-44-440000000000000000000000000000000000000000000000000000000000000000000000

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