Finite Group Databasebeta

← Group #10858854

Character table — Group #10858854

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order12222222222234444666666644444466661212121244444412121212121212121212121212121212121244448888888844121212124444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111-11111-1-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-11111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ911111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-11-111-1-111-1-1-1-111-1-1
χ1011111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-11111-1-111
χ1111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-11-1-11111-1-1-1-1-1-111
χ1211111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-1111111-1-1
χ1311111111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-111-1-1111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-11-1-111-1-111-1-1-1-111
χ1411111111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-111-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-11111-1-1
χ1511111111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111-111-1-1-1-111-1-111-1-1
χ1611111111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-111-1-111
χ172222222222222-2-2-2-222222222222-2-22222-2-2-2-2-20000-2-2-2-2-22222-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-22222-2-2-2-220000222-2-2-2-2-2-222000000000000000000000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ20222222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-2-2-2-22-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ21222222222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-22222-211-1-1111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ22222222222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-211-1-11111111111111100000000000022-1-1-1-10000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-11111-20000-21111-1-1-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-11111-20000-21111-1-1-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111200002-1-1111111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111200002-1-1111111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ2722222222-2-2-2-22-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-2-200002222222-2-2-2-2000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-220000-2-2-222-2-22222000000000000000000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-122-2-2-2-21111-1-1-1-1222-2-2-21111-1-111-1-1-1-1-1-111110000000000002-2-1-1110000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-122-2-2-2-21111-1-1-1-12-2-222-21111-1-111-1-11111-1-1-1-1000000000000-2211-1-10000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1-222-2-22-1-11111-1-111-1-1-1-11111000000000000-2211-1-10000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1-2-2-2222-1-11111-1-1111111-1-1-1-10000000000002-2-1-1110000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-22211111111-200002-1-1-1-1-1-11111−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i30000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-22211111111-200002-1-1-1-1-1-11111i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i30000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-222221111111120000-211-1-111-1-1-1-1−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i30000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-222221111111120000-211-1-111-1-1-1-1i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i30000000000
χ3722-2-22-2-2222-2-2200002-22-2-2-222i−2i2i−2i0022-2-2000000000000002i−2i2i−2i0000000000000022−2−222−2−2000000000000−i2i2−i2i2
χ3822-2-22-2-2222-2-2200002-22-2-2-222i−2i2i−2i0022-2-2000000000000002i−2i2i−2i00000000000000−2−222−2−222000000000000i2−i2i2−i2
χ3922-2-22-2-2222-2-2200002-22-2-2-22−2i2i−2i2i0022-2-200000000000000−2i2i−2i2i0000000000000022−2−222−2−2000000000000i2−i2i2−i2
χ4022-2-22-2-2222-2-2200002-22-2-2-22−2i2i−2i2i0022-2-200000000000000−2i2i−2i2i00000000000000−2−222−2−222000000000000−i2i2−i2i2
χ4122-2-22-2-22-2-222200002-22-2-2-222i−2i−2i2i00-2-222000000000000002i−2i−2i2i0000000000000022−2−2−2−222000000000000−i2i2i2−i2
χ4222-2-22-2-22-2-222200002-22-2-2-222i−2i−2i2i00-2-222000000000000002i−2i−2i2i00000000000000−2−22222−2−2000000000000i2−i2−i2i2
χ4322-2-22-2-22-2-222200002-22-2-2-22−2i2i2i−2i00-2-22200000000000000−2i2i2i−2i0000000000000022−2−2−2−222000000000000i2−i2−i2i2
χ4422-2-22-2-22-2-222200002-22-2-2-22−2i2i2i−2i00-2-22200000000000000−2i2i2i−2i00000000000000−2−22222−2−2000000000000−i2i2i2−i2
χ4522-2-2-222-22-22-2222-2-222-22-2-2-200002-22-22-222-2-2000000002-2000000000000000000000000000000002-22-2000000
χ4622-2-2-222-22-22-2222-2-222-22-2-2-200002-22-22-222-2-2000000002-200000000000000000000000000000000-22-22000000
χ4722-2-2-222-22-22-22-2-22222-22-2-2-20000-222-22-2-2-22200000000-22000000000000002i2i−2i−2i0000000000000000002i−2i0000
χ4822-2-2-222-22-22-22-2-22222-22-2-2-20000-222-22-2-2-22200000000-2200000000000000−2i−2i2i2i000000000000000000−2i2i0000
χ4922-2-2-222-2-22-22222-2-222-22-2-2-20000-22-22-2222-2-200000000-22000000000000000000000000000000002-2-22000000
χ5022-2-2-222-2-22-22222-2-222-22-2-2-20000-22-22-2222-2-200000000-2200000000000000000000000000000000-222-2000000
χ5122-2-2-222-2-22-222-2-22222-22-2-2-200002-2-22-22-2-222000000002-2000000000000002i2i−2i−2i000000000000000000−2i2i0000
χ5222-2-2-222-2-22-222-2-22222-22-2-2-200002-2-22-22-2-222000000002-200000000000000−2i−2i2i2i0000000000000000002i−2i0000
χ532-22-22-22-2000022-22-2-2-2-222-2200000000002-22-20002-20000000000000002-22-22i−2i2i−2i00002i−2i2i−2i0000000000000000
χ542-22-22-22-2000022-22-2-2-2-222-2200000000002-22-20002-20000000000000002-22-2−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ552-22-22-22-2000022-22-2-2-2-222-2200000000002-22-2000-22000000000000000-22-222i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ562-22-22-22-2000022-22-2-2-2-222-2200000000002-22-2000-22000000000000000-22-22−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ572-2-22-2-22200002-222-2-2-222-22-20000000000-222-202i−2i00000000000002i−2i2i−2i00002-2-222i−2i2i−2i00000000000000000000
χ582-2-22-2-22200002-222-2-2-222-22-20000000000-222-202i−2i00000000000002i−2i2i−2i0000-222-2−2i2i−2i2i00000000000000000000
χ592-2-22-2-22200002-222-2-2-222-22-20000000000-222-20−2i2i0000000000000−2i2i−2i2i00002-2-22−2i2i−2i2i00000000000000000000
χ602-2-22-2-22200002-222-2-2-222-22-20000000000-222-20−2i2i0000000000000−2i2i−2i2i0000-222-22i−2i2i−2i00000000000000000000
χ614444-4-4-4-44-4-44400004-4-4-444-40000004-4-4400000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-44-4-44-20000-2222-2-22000000-222-2000000000023−2300000023−23000000000000000000000000000000000000
χ634444-4-4-4-44-4-44-20000-2222-2-22000000-222-20000000000−2323000000−2323000000000000000000000000000000000000
χ644444-4-4-4-4-444-4400004-4-4-444-4000000-444-400000000000000000000000000000000000000000000000000000000
χ654444-4-4-4-4-444-4-20000-2222-2-220000002-2-22000000000023−23000000−2323000000000000000000000000000000000000
χ664444-4-4-4-4-444-4-20000-2222-2-220000002-2-220000000000−232300000023−23000000000000000000000000000000000000
χ6744-4-44-4-4444-4-4-20000-22-2222-24i−4i4i−4i00-2-22200000000000000−2i2i−2i2i00000000000000000000000000000000000000
χ6844-4-44-4-4444-4-4-20000-22-2222-2−4i4i−4i4i00-2-222000000000000002i−2i2i−2i00000000000000000000000000000000000000
χ6944-4-44-4-44-4-444-20000-22-2222-24i−4i−4i4i0022-2-200000000000000−2i2i2i−2i00000000000000000000000000000000000000
χ7044-4-44-4-44-4-444-20000-22-2222-2−4i4i4i−4i0022-2-2000000000000002i−2i−2i2i00000000000000000000000000000000000000
χ7144-4-4-444-44-44-4-244-4-4-2-22-222200004-4-22-22-2-22200000000-22000000000000000000000000000000000000000000
χ7244-4-4-444-44-44-4-2-4-444-2-22-22220000-44-22-2222-2-2000000002-2000000000000000000000000000000000000000000
χ7344-4-4-444-4-44-44-244-4-4-2-22-22220000-442-22-2-2-222000000002-2000000000000000000000000000000000000000000
χ7444-4-4-444-4-44-44-2-4-444-2-22-222200004-42-22-222-2-200000000-22000000000000000000000000000000000000000000
χ754-44-44-44-400004-44-44-4-4-444-440000000000-44-440000000000000000000000000000000000000000000000000000
χ764-44-44-44-40000-24-44-4222-2-22-20000000000-22-220004-4000000000000000-22-220000000000000000000000000000
χ774-44-44-44-40000-24-44-4222-2-22-20000000000-22-22000-440000000000000002-22-20000000000000000000000000000
χ784-44-44-44-40000-2-44-44222-2-22-200000000002-22-200000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ794-44-44-44-40000-2-44-44222-2-22-200000000002-22-2000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ804-44-4-44-44000040000-444-44-4-4000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ814-44-4-44-44000040000-444-44-4-40000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ824-4-4444-4-4000040000-44-4-4-4440000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ834-4-4444-4-4000040000-44-4-4-44400000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ844-4-44-4-444000044-4-44-4-444-44-400000000004-4-440000000000000000000000000000000000000000000000000000
χ854-4-44-4-4440000-24-4-4422-2-22-220000000000-222-2000000000000000023−23−232300000000000000000000000000000000
χ864-4-44-4-4440000-24-4-4422-2-22-220000000000-222-20000000000000000−232323−2300000000000000000000000000000000
χ874-4-44-4-4440000-2-444-422-2-22-2200000000002-2-2204i−4i0000000000000−2i2i−2i2i00000000000000000000000000000000
χ884-4-44-4-4440000-2-444-422-2-22-2200000000002-2-220−4i4i00000000000002i−2i2i−2i00000000000000000000000000000000
χ898-88-8-88-880000-400004-4-44-444000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8888-8-80000-400004-4444-4-4000000000000000000000000000000000000000000000000000000000000000000

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