Finite Group Databasebeta

← Group #10858330

Character table — Group #10858330

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121244444412121212121212121212121212121212121244448888888844121212124444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-11-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111-111-111-1-1-1-1-1-1111111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-111-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1
χ9111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-1-1-111
χ10111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-1111111-1-1
χ11111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111-111-1-111-1-1-1-111-1-1
χ12111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-11111-1-111
χ13111111111-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1111-1-1-1-111-1-11111-1-111-1-1-1-111111111-1-1-1-11-111-1-1-1-1-1-11111-1-1
χ14111111111-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-11111-1-1-1-111
χ15111111111-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-11-1-111-1-1-1-111-1-111
χ16111111111-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-1-1111111-1-111-1-1
χ172222222222222-2-2-2-222222222222-2-22222-2-2-2-2-200-2002222-2-20000-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-22222-2-2-2-2200200-2-2-2-2220000-2-22200000000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-2-20020022-2-2-2-20000222200000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2200-200-2-22222000022-2-200000000000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-1-11111-1-1-1-11111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-222-222111111-1-1-1-1-1-111-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111111-1-111111100000000000022-1-1-1-10000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-11111-200-200-1-1-1-111−i3−i3i3i31111−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-11111-200-200-1-1-1-111i3i3−i3−i31111i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-111112002001111-1-1−i3−i3i3i311-1-1−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-111112002001111-1-1i3i3−i3−i311-1-1i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-21111-1-1-1-1222-2-2-2-1-111-1-1-1-1-1-111111111000000000000-2211-1-10000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-21111-1-1-1-12-2-2-222-1-111-1-111111111-1-1-1-10000000000002-2-1-1110000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1-2222-2-211-1-111-1-1-1-111-1-111110000000000002-2-1-1110000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1-2-2-222211-1-111111111-1-1-1-1-1-1000000000000-2211-1-10000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-22211111111-200200-1-11111−i3−i3i3i3-1-1-1-1i3i3−i3−i300000000000000i3−i3−i3i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-22211111111-200200-1-11111i3i3−i3−i3-1-1-1-1−i3−i3i3i300000000000000−i3i3i3−i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222211111111200-20011-1-1-1-1−i3−i3i3i3-1-111i3i3−i3−i300000000000000−i3i3i3−i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222211111111200-20011-1-1-1-1i3i3−i3−i3-1-111−i3−i3i3i300000000000000i3−i3−i3i30000000000
χ37222-2-22-2-22000022-2-222-2-22-2-2000000000022-2-202-20000000002-22-20000000022-2-222-2-200000000000000000000
χ38222-2-22-2-22000022-2-222-2-22-2-2000000000022-2-202-20000000002-22-200000000-2-222-2-22200000000000000000000
χ39222-2-22-2-22000022-2-222-2-22-2-2000000000022-2-20-22000000000-22-220000000022-2-2-2-22200000000000000000000
χ40222-2-22-2-22000022-2-222-2-22-2-2000000000022-2-20-22000000000-22-2200000000-2-22222-2-200000000000000000000
χ4122-222-2-2-2222-2-200002-222-2-2-22-22-20022-2-200000000002-22-20000000000000000002−22−222−2−20000000000002−22−2
χ4222-222-2-2-2222-2-200002-222-2-2-22-22-20022-2-200000000002-22-2000000000000000000−22−22−2−222000000000000−22−22
χ4322-222-2-2-2222-2-200002-222-2-2-2-22-220022-2-20000000000-22-220000000000000000002−22−222−2−2000000000000−22−22
χ4422-222-2-2-2222-2-200002-222-2-2-2-22-220022-2-20000000000-22-22000000000000000000−22−22−2−2220000000000002−22−2
χ4522-222-2-2-22-2-22200002-222-2-2-22-2-2200-2-22200000000002-2-220000000000000000002−22−2−2−222000000000000−222−2
χ4622-222-2-2-22-2-22200002-222-2-2-22-2-2200-2-22200000000002-2-22000000000000000000−22−2222−2−20000000000002−2−22
χ4722-222-2-2-22-2-22200002-222-2-2-2-222-200-2-2220000000000-222-20000000000000000002−22−2−2−2220000000000002−2−22
χ4822-222-2-2-22-2-22200002-222-2-2-2-222-200-2-2220000000000-222-2000000000000000000−22−2222−2−2000000000000−222−2
χ492-2-22-222-222i−2i2i−2i2-2-22-2-22-222-200002i−2i2i−2i2i−2i2-22-200000000000000002i−2i0000000000000000000000002-2002i−2i0000
χ502-2-22-222-222i−2i2i−2i2-2-22-2-22-222-200002i−2i2i−2i2i−2i2-22-200000000000000002i−2i000000000000000000000000-2200−2i2i0000
χ512-2-22-222-222i−2i2i−2i-222-2-2-22-222-20000−2i2i2i−2i2i−2i-22-220000000000000000−2i2i0000002-22-200000000000000002i−2i000000
χ522-2-22-222-222i−2i2i−2i-222-2-2-22-222-20000−2i2i2i−2i2i−2i-22-220000000000000000−2i2i000000-22-220000000000000000−2i2i000000
χ532-2-22-222-22−2i2i−2i2i2-2-22-2-22-222-20000−2i2i−2i2i−2i2i2-22-20000000000000000−2i2i0000000000000000000000002-200−2i2i0000
χ542-2-22-222-22−2i2i−2i2i2-2-22-2-22-222-20000−2i2i−2i2i−2i2i2-22-20000000000000000−2i2i000000000000000000000000-22002i−2i0000
χ552-2-22-222-22−2i2i−2i2i-222-2-2-22-222-200002i−2i−2i2i−2i2i-22-2200000000000000002i−2i0000002-22-20000000000000000−2i2i000000
χ562-2-22-222-22−2i2i−2i2i-222-2-2-22-222-200002i−2i−2i2i−2i2i-22-2200000000000000002i−2i000000-22-2200000000000000002i−2i000000
χ572-2-2-222-2220000-22-22-2-2-222-220000000000-222-200002-2000000000000002-22-22-2-2200002-22-20000000000000000
χ582-2-2-222-2220000-22-22-2-2-222-220000000000-222-200002-2000000000000002-22-2-222-20000-22-220000000000000000
χ592-2-2-222-2220000-22-22-2-2-222-220000000000-222-20000-2200000000000000-22-222-2-220000-22-220000000000000000
χ602-2-2-222-2220000-22-22-2-2-222-220000000000-222-20000-2200000000000000-22-22-222-200002-22-20000000000000000
χ61444-4-44-4-440000-4-44444-4-44-4-40000000000-4-4440000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-2000044-4-4-2-222-2220000000000-2-22204-4000000000-22-22000000000000000000000000000000000000
χ63444-4-44-4-4-2000044-4-4-2-222-2220000000000-2-2220-440000000002-22-2000000000000000000000000000000000000
χ64444-4-44-4-4-20000-4-444-2-222-222000000000022-2-2000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ65444-4-44-4-4-20000-4-444-2-222-222000000000022-2-20000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ6644-444-4-4-4-244-4-40000-22-2-22224-44-400-2-2220000000000-22-22000000000000000000000000000000000000000000
χ6744-444-4-4-4-244-4-40000-22-2-2222-44-4400-2-22200000000002-22-2000000000000000000000000000000000000000000
χ6844-444-4-4-4-2-4-4440000-22-2-22224-4-440022-2-20000000000-222-2000000000000000000000000000000000000000000
χ6944-444-4-4-4-2-4-4440000-22-2-2222-444-40022-2-200000000002-2-22000000000000000000000000000000000000000000
χ7044-4-4-4-4444000000004-4-4-4-44400000000000000000000000000000000000000000022−22−222200000000000000000000
χ7144-4-4-4-4444000000004-4-4-4-444000000000000000000000000000000000000000000−222222−2200000000000000000000
χ724-444-4-4-4444i−4i−4i4i0000-444-4-4-440000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ734-444-4-4-444−4i4i4i−4i0000-444-4-4-44000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ744-444-4-4-44-24i−4i−4i4i00002-2-2222-2000000−2i2i2i−2i0000000000000023−23000000−2i32i300000000000000000000000000000000
χ754-444-4-4-44-24i−4i−4i4i00002-2-2222-2000000−2i2i2i−2i00000000000000−23230000002i3−2i300000000000000000000000000000000
χ764-444-4-4-44-2−4i4i4i−4i00002-2-2222-20000002i−2i−2i2i0000000000000023−230000002i3−2i300000000000000000000000000000000
χ774-444-4-4-44-2−4i4i4i−4i00002-2-2222-20000002i−2i−2i2i00000000000000−2323000000−2i32i300000000000000000000000000000000
χ784-44-44-44-4400000000-44-44-44-4000000000000000000000000000000000000000000000022−22−22220000000000000000
χ794-44-44-44-4400000000-44-44-44-40000000000000000000000000000000000000000000000−222222−220000000000000000
χ804-4-44-444-4-24i−4i4i−4i4-4-4422-22-2-2200004i−4i−2i2i−2i2i-22-220000000000000000−2i2i0000000000000000000000000000000000
χ814-4-44-444-4-24i−4i4i−4i-444-422-22-2-220000−4i4i−2i2i−2i2i2-22-200000000000000002i−2i0000000000000000000000000000000000
χ824-4-44-444-4-2−4i4i−4i4i4-4-4422-22-2-220000−4i4i2i−2i2i−2i-22-2200000000000000002i−2i0000000000000000000000000000000000
χ834-4-44-444-4-2−4i4i−4i4i-444-422-22-2-2200004i−4i2i−2i2i−2i2-22-20000000000000000−2i2i0000000000000000000000000000000000
χ844-4-4-444-44400004-44-4-4-4-444-4400000000004-4-440000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-200004-44-4222-2-22-20000000000-222-200000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ864-4-4-444-44-200004-44-4222-2-22-20000000000-222-2000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ874-4-4-444-44-20000-44-44222-2-22-200000000002-2-2200004-400000000000000-22-220000000000000000000000000000
χ884-4-4-444-44-20000-44-44222-2-22-200000000002-2-220000-44000000000000002-22-20000000000000000000000000000
χ8988-8-8-8-888-400000000-44444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-8-4000000004-44-44-44000000000000000000000000000000000000000000000000000000000000000000

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