Finite Group Databasebeta

← Group #10822607

Character table — Group #10822607

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222444488888888888822224444448888161616161616161616161616333366666612121212242424242424242424242424
order12442224444444244444448888361212666121212121212126121212121212122424242422442224444444244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111
χ311111111111111-1-111-1-1-1-111-1-111111111111111-1-111-1-1-1-111-1-111111111111111-1-111-1-1-1-111-1-1
χ411111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1
χ51111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1
χ61111111111-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-111-1-1-1-11111-1-1
χ71111111111-1-1-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-111-1-111-1-111
χ81111111111-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-111-1-11111
χ922222-2-2-2-220000002i−2i0000000022222-2-2-2-220000002i−2i0000000022222-2-2-2-220000002i−2i00000000
χ1022222-2-2-2-22000000−2i2i0000000022222-2-2-2-22000000−2i2i0000000022222-2-2-2-22000000−2i2i00000000
χ112222-22-22-2-2000000000000002i−2i2222-22-22-2-2000000000000002i−2i2222-22-22-2-2000000000000002i−2i
χ122222-22-22-2-200000000000000−2i2i2222-22-22-2-200000000000000−2i2i2222-22-22-2-200000000000000−2i2i
χ132222-2-22-22-200000000002-200002222-2-22-22-200000000002-200002222-2-22-22-200000000002-20000
χ142222-2-22-22-20000000000-2200002222-2-22-22-20000000000-2200002222-2-22-22-20000000000-220000
χ1522-2-2222-2-2-2000000002-200000022-2-2222-2-2-2000000002-200000022-2-2222-2-2-2000000002-2000000
χ1622-2-2222-2-2-200000000-2200000022-2-2222-2-2-200000000-2200000022-2-2222-2-2-200000000-22000000
χ1722-2-22-2-222-200002-2000000000022-2-22-2-222-200002-2000000000022-2-22-2-222-200002-20000000000
χ1822-2-22-2-222-20000-22000000000022-2-22-2-222-20000-22000000000022-2-22-2-222-20000-220000000000
χ1922-2-2-22-2-2220000000000002i−2i0022-2-2-22-2-2220000000000002i−2i0022-2-2-22-2-2220000000000002i−2i00
χ2022-2-2-22-2-222000000000000−2i2i0022-2-2-22-2-222000000000000−2i2i0022-2-2-22-2-222000000000000−2i2i00
χ2122-2-2-2-222-2222-2-200000000000022-2-2-2-222-2222-2-200000000000022-2-2-2-222-2222-2-2000000000000
χ2222-2-2-2-222-22-2-22200000000000022-2-2-2-222-22-2-22200000000000022-2-2-2-222-22-2-222000000000000
χ234-44i−4i0000002-22i−2i0000000000004-44i−4i0000002-22i−2i0000000000004-44i−4i0000002-22i−2i000000000000
χ244-44i−4i000000-22−2i2i0000000000004-44i−4i000000-22−2i2i0000000000004-44i−4i000000-22−2i2i000000000000
χ254-4−4i4i0000002-2−2i2i0000000000004-4−4i4i0000002-2−2i2i0000000000004-4−4i4i0000002-2−2i2i000000000000
χ264-4−4i4i000000-222i−2i0000000000004-4−4i4i000000-222i−2i0000000000004-4−4i4i000000-222i−2i000000000000
χ271111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ281111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ2911111111111111-1-111-1-1-1-111-1-111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ3011111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ311111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ321111111111-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ331111111111-1-1-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ341111111111-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ3522222-2-2-2-220000002i−2i0000000022222-2-2-2-220000002i−2i00000000-2-2-2-2-22222-2000000−2i2i00000000
χ3622222-2-2-2-22000000−2i2i0000000022222-2-2-2-22000000−2i2i00000000-2-2-2-2-22222-20000002i−2i00000000
χ372222-22-22-2-2000000000000002i−2i2222-22-22-2-2000000000000002i−2i-2-2-2-22-22-22200000000000000−2i2i
χ382222-22-22-2-200000000000000−2i2i2222-22-22-2-200000000000000−2i2i-2-2-2-22-22-222000000000000002i−2i
χ392222-2-22-22-200000000002-200002222-2-22-22-200000000002-20000-2-2-2-222-22-220000000000-220000
χ402222-2-22-22-20000000000-2200002222-2-22-22-20000000000-220000-2-2-2-222-22-2200000000002-20000
χ4122-2-2222-2-2-2000000002-200000022-2-2222-2-2-2000000002-2000000-2-222-2-2-222200000000-22000000
χ4222-2-2222-2-2-200000000-2200000022-2-2222-2-2-200000000-22000000-2-222-2-2-2222000000002-2000000
χ4322-2-22-2-222-200002-2000000000022-2-22-2-222-200002-20000000000-2-222-222-2-220000-220000000000
χ4422-2-22-2-222-20000-22000000000022-2-22-2-222-20000-220000000000-2-222-222-2-2200002-20000000000
χ4522-2-2-22-2-2220000000000002i−2i0022-2-2-22-2-2220000000000002i−2i00-2-2222-222-2-2000000000000−2i2i00
χ4622-2-2-22-2-222000000000000−2i2i0022-2-2-22-2-222000000000000−2i2i00-2-2222-222-2-20000000000002i−2i00
χ4722-2-2-2-222-2222-2-200000000000022-2-2-2-222-2222-2-2000000000000-2-22222-2-22-2-2-222000000000000
χ4822-2-2-2-222-22-2-22200000000000022-2-2-2-222-22-2-222000000000000-2-22222-2-22-222-2-2000000000000
χ494-44i−4i0000002-22i−2i0000000000004-44i−4i0000002-22i−2i000000000000-44−4i4i000000-22−2i2i000000000000
χ504-44i−4i000000-22−2i2i0000000000004-44i−4i000000-22−2i2i000000000000-44−4i4i0000002-22i−2i000000000000
χ514-4−4i4i0000002-2−2i2i0000000000004-4−4i4i0000002-2−2i2i000000000000-444i−4i000000-222i−2i000000000000
χ524-4−4i4i000000-222i−2i0000000000004-4−4i4i000000-222i−2i000000000000-444i−4i0000002-2−2i2i000000000000
χ5322222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ542222222222222222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-100000000000000000000000000
χ5522222222222222-2-222-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11100000000000000000000000000
χ5622222222222222-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000000000
χ572222222222-2-2-2-2222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111100000000000000000000000000
χ582222222222-2-2-2-222-2-2-2-22222-2-2-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11100000000000000000000000000
χ592222222222-2-2-2-2-2-222-2-222-2-222-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-100000000000000000000000000
χ602222222222-2-2-2-2-2-2-2-222-2-22222-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-100000000000000000000000000
χ6144444-4-4-4-440000004i−4i00000000-2-2-2-2-22222-2000000−2i2i0000000000000000000000000000000000
χ6244444-4-4-4-44000000−4i4i00000000-2-2-2-2-22222-20000002i−2i0000000000000000000000000000000000
χ634444-44-44-4-4000000000000004i−4i-2-2-2-22-22-22200000000000000−2i2i00000000000000000000000000
χ644444-44-44-4-400000000000000−4i4i-2-2-2-22-22-222000000000000002i−2i00000000000000000000000000
χ654444-4-44-44-400000000004-40000-2-2-2-222-22-220000000000-22000000000000000000000000000000
χ664444-4-44-44-40000000000-440000-2-2-2-222-22-2200000000002-2000000000000000000000000000000
χ6744-4-4444-4-4-4000000004-4000000-2-222-2-2-222200000000-2200000000000000000000000000000000
χ6844-4-4444-4-4-400000000-44000000-2-222-2-2-2222000000002-200000000000000000000000000000000
χ6944-4-44-4-444-400004-40000000000-2-222-222-2-220000-22000000000000000000000000000000000000
χ7044-4-44-4-444-40000-440000000000-2-222-222-2-2200002-2000000000000000000000000000000000000
χ7144-4-4-44-4-4440000000000004i−4i00-2-2222-222-2-2000000000000−2i2i0000000000000000000000000000
χ7244-4-4-44-4-444000000000000−4i4i00-2-2222-222-2-20000000000002i−2i0000000000000000000000000000
χ7344-4-4-4-444-4444-4-4000000000000-2-22222-2-22-2-2-22200000000000000000000000000000000000000
χ7444-4-4-4-444-44-4-444000000000000-2-22222-2-22-222-2-200000000000000000000000000000000000000
χ758-88i−8i0000004-44i−4i000000000000-44−4i4i000000-22−2i2i00000000000000000000000000000000000000
χ768-88i−8i000000-44−4i4i000000000000-44−4i4i0000002-22i−2i00000000000000000000000000000000000000
χ778-8−8i8i0000004-4−4i4i000000000000-444i−4i000000-222i−2i00000000000000000000000000000000000000
χ788-8−8i8i000000-444i−4i000000000000-444i−4i0000002-2−2i2i00000000000000000000000000000000000000

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