Finite Group Databasebeta

← Group #10830003

Character table — Group #10830003

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
χ31111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1
χ9111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11-111-1-1-1-111-1-111-1-1
χ10111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-111-1-111-1-111-1-111
χ11111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-11-1-1-11111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-111-1-1-1-111
χ12111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-11-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11111-1-11111-1-1
χ13111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-111-1-1-1-111-1-111
χ14111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-1111111-1-111-1-1
χ15111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1-11-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111111-111-1-1-1-1-1-11111-1-1
χ16111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1-11-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-11111-1-1-1-111
χ172222222222222-2-2-2-222222222222-2-2-2-2-2-22222-2-2000022220000-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222220000-2-2-2-20000-2-2222200000000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-2-22000022-2-2000022-2-22200000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-22-20000-2-22200002222-2-200000000000000000000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111-1-1-1-1-1-11111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-222221111-1-1-1-1-1-11111-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111-1-11111111100000000000022-1-1-1-10000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-20000-1-1-1-1−i3−i3i3i3111111−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-20000-1-1-1-1i3i3−i3−i3111111i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12200001111−i3−i3i3i311-1-1-1-1−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12200001111i3i3−i3−i311-1-1-1-1i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-111112-222-2-2-1-111111111-1-111-1-1-1-10000000000002-2-1-1110000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-111112-2-2-222-1-111-1-1-1-111-1-1111111000000000000-2211-1-10000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111-2222-2-211-1-111111111-1-1-1-1-1-1000000000000-2211-1-10000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111-22-2-22211-1-1-1-1-1-11111-1-111110000000000002-2-1-1110000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-22211111111-220000-1-111−i3−i3i3i3-1-111-1-1i3i3−i3−i300000000000000i3−i3−i3i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-22211111111-220000-1-111i3i3−i3−i3-1-111-1-1−i3−i3i3i300000000000000−i3i3i3−i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222111111112-2000011-1-1−i3−i3i3i3-1-1-1-111i3i3−i3−i300000000000000−i3i3i3−i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222111111112-2000011-1-1i3i3−i3−i3-1-1-1-111−i3−i3i3i300000000000000i3−i3−i3i30000000000
χ37222-22-2-2-2222-2-2000022-22-2-2-22-22-200000022-2-20000002-22-200000000000000000022−2−222−2−20000000000002−22−2
χ38222-22-2-2-2222-2-2000022-22-2-2-22-22-200000022-2-20000002-22-2000000000000000000−2−222−2−222000000000000−22−22
χ39222-22-2-2-2222-2-2000022-22-2-2-2-22-2200000022-2-2000000-22-2200000000000000000022−2−222−2−2000000000000−22−22
χ40222-22-2-2-2222-2-2000022-22-2-2-2-22-2200000022-2-2000000-22-22000000000000000000−2−222−2−2220000000000002−22−2
χ41222-22-2-2-22-2-222000022-22-2-2-22-2-22000000-2-2220000002-2-2200000000000000000022−2−2−2−2220000000000002−2−22
χ42222-22-2-2-22-2-222000022-22-2-2-22-2-22000000-2-2220000002-2-22000000000000000000−2−22222−2−2000000000000−222−2
χ43222-22-2-2-22-2-222000022-22-2-2-2-222-2000000-2-222000000-222-200000000000000000022−2−2−2−222000000000000−222−2
χ44222-22-2-2-22-2-222000022-22-2-2-2-222-2000000-2-222000000-222-2000000000000000000−2−22222−2−20000000000002−2−22
χ4522-22-2-2-2220000-22-222-22-22-2-200000022-2-2000000002-200002-22-200000000002i2i−2i−2i00002i−2i2i−2i0000000000000000
χ4622-22-2-2-2220000-22-222-22-22-2-200000022-2-2000000002-200002-22-20000000000−2i−2i2i2i0000−2i2i−2i2i0000000000000000
χ4722-22-2-2-2220000-22-222-22-22-2-200000022-2-200000000-220000-22-2200000000002i2i−2i−2i0000−2i2i−2i2i0000000000000000
χ4822-22-2-2-2220000-22-222-22-22-2-200000022-2-200000000-220000-22-220000000000−2i−2i2i2i00002i−2i2i−2i0000000000000000
χ492-22-2-22-222000022-2-2-22-2-222-20000002-22-20000002i−2i00000000000000002i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000
χ502-22-2-22-222000022-2-2-22-2-222-20000002-22-20000002i−2i00000000000000002i−2i2i−2i−2i2i−2i2i-22-2200000000000000000000
χ512-22-2-22-222000022-2-2-22-2-222-20000002-22-2000000−2i2i0000000000000000−2i2i−2i2i2i−2i2i−2i-22-2200000000000000000000
χ522-22-2-22-222000022-2-2-22-2-222-20000002-22-2000000−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000
χ532-2-2-22-22222-22-22-2-22-2-2-222-2200002-2-222-22-22-2000000000000002-200000000000000000000000000002-22-20000
χ542-2-2-22-22222-22-22-2-22-2-2-222-2200002-2-222-22-22-2000000000000002-20000000000000000000000000000-22-220000
χ552-2-2-22-22222-22-2-222-2-2-2-222-220000-222-2-222-22-200000000000000-22000000002-2-22000000000000002-200000000
χ562-2-2-22-22222-22-2-222-2-2-2-222-220000-222-2-222-22-200000000000000-2200000000-222-200000000000000-2200000000
χ572-2-2-22-2222-22-222-2-22-2-2-222-220000-22-222-2-22-2200000000000000-2200000000000000000000000000002-2-220000
χ582-2-2-22-2222-22-222-2-22-2-2-222-220000-22-222-2-22-2200000000000000-220000000000000000000000000000-222-20000
χ592-2-2-22-2222-22-22-222-2-2-2-222-2200002-22-2-22-22-22000000000000002-2000000002-2-2200000000000000-2200000000
χ602-2-2-22-2222-22-22-222-2-2-2-222-2200002-22-2-22-22-22000000000000002-200000000-222-2000000000000002-200000000
χ61444-44-4-4-4-244-4-40000-2-22-22224-44-4000000-2-222000000-22-22000000000000000000000000000000000000000000
χ62444-44-4-4-4-244-4-40000-2-22-2222-44-44000000-2-2220000002-22-2000000000000000000000000000000000000000000
χ63444-44-4-4-4-2-4-4440000-2-22-22224-4-4400000022-2-2000000-222-2000000000000000000000000000000000000000000
χ64444-44-4-4-4-2-4-4440000-2-22-2222-444-400000022-2-20000002-2-22000000000000000000000000000000000000000000
χ6544-44-4-4-44400004-44-44-44-44-4-4000000-4-44400000000000000000000000000000000000000000000000000000000
χ6644-44-4-4-44-200004-44-4-22-22-22200000022-2-200000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ6744-44-4-4-44-200004-44-4-22-22-22200000022-2-2000000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ6844-44-4-4-44-20000-44-44-22-22-222000000-2-222000000004-40000-22-2200000000000000000000000000000000000000
χ6944-44-4-4-44-20000-44-44-22-22-222000000-2-22200000000-4400002-22-200000000000000000000000000000000000000
χ7044-4-4-444-44000000004-4-4-4-4440000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ7144-4-4-444-44000000004-4-4-4-44400000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ724-444-4-44-4400000000-444-4-4-4400000000000000000000000000000000000000000022−22−222200000000000000000000
χ734-444-4-44-4400000000-444-4-4-44000000000000000000000000000000000000000000−222222−2200000000000000000000
χ744-44-4-44-4440000-4-444-44-4-444-4000000-44-4400000000000000000000000000000000000000000000000000000000
χ754-44-4-44-44-2000044-4-42-222-2-22000000-22-220000004i−4i0000000000000000−2i2i−2i2i0000000000000000000000000000
χ764-44-4-44-44-2000044-4-42-222-2-22000000-22-22000000−4i4i00000000000000002i−2i2i−2i0000000000000000000000000000
χ774-44-4-44-44-20000-4-4442-222-2-220000002-22-200000000000000000000000023−23−23230000000000000000000000000000
χ784-44-4-44-44-20000-4-4442-222-2-220000002-22-2000000000000000000000000−232323−230000000000000000000000000000
χ794-4-4444-4-444-4-440000-4-444-44-400000000004-4-440000000000000000000000000000000000000000000000000000
χ804-4-4444-4-44-444-40000-4-444-44-40000000000-444-40000000000000000000000000000000000000000000000000000
χ814-4-4444-4-4-24-4-44000022-2-22-220000000000-222-2000000000000000023−2323−2300000000000000000000000000000000
χ824-4-4444-4-4-24-4-44000022-2-22-220000000000-222-20000000000000000−2323−232300000000000000000000000000000000
χ834-4-4444-4-4-2-444-4000022-2-22-2200000000002-2-22000000000000000023−23−232300000000000000000000000000000000
χ844-4-4444-4-4-2-444-4000022-2-22-2200000000002-2-220000000000000000−232323−2300000000000000000000000000000000
χ854-4-4-44-444-24-44-44-4-44222-2-22-200004-42-2-22-22-2200000000000000-22000000000000000000000000000000000000
χ864-4-4-44-444-24-44-4-444-4222-2-22-20000-44-222-2-22-22000000000000002-2000000000000000000000000000000000000
χ874-4-4-44-444-2-44-444-4-44222-2-22-20000-442-2-222-22-2000000000000002-2000000000000000000000000000000000000
χ884-4-4-44-444-2-44-44-444-4222-2-22-200004-4-222-22-22-200000000000000-22000000000000000000000000000000000000
χ8988-8-8-888-8-400000000-44444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ908-888-8-88-8-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000

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