Finite Group Databasebeta

← Group #10696020

Character table — Group #10696020

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222222222444444444488881616161616161616161616161616161616162424242424242424242424244848
order12222234444666444466121212121212121244448812121212121212122424242444444444888888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-11-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111-11-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ9222222222-2-22222-2-2-222-2-2222-2-2-2020-200002200-2-2000000000000000000
χ10222222222-2-22222-2-2-222-2-2222-2-2-20-2020000-2-20022000000000000000000
χ112222222-2-222222-22-2-22222-2-2-22-2-2000000000000000000000022-2-2000000
χ122222222-2-222222-22-2-22222-2-2-22-2-20000000000000000000000-2-222000000
χ132222222-2-2-2-2222-2-22222-2-2-2-2-2-22200000000000000000022-2-20000000000
χ142222222-2-2-2-2222-2-22222-2-2-2-2-2-222000000000000000000-2-2220000000000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12-22-2-2-2-1-111-1-111111100000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-22-22-2-211-1-111-1-1111100000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-100000000000000
χ19222222-122-2-2-1-1-12-2-2-2-1-111-1-1-1111020-200−i3i3-1-1−i3i311−i3−i3i3i300000000000000
χ20222222-122-2-2-1-1-12-2-2-2-1-111-1-1-1111020-200i3−i3-1-1i3−i311i3i3−i3−i300000000000000
χ21222222-122-2-2-1-1-12-2-2-2-1-111-1-1-11110-20200−i3i311−i3i3-1-1i3i3−i3−i300000000000000
χ22222222-122-2-2-1-1-12-2-2-2-1-111-1-1-11110-20200i3−i311i3−i3-1-1−i3−i3i3i300000000000000
χ232222-2-222222222-2-22-2-2-22222-2-22-200002-2000000002-22-200000000000000
χ242222-2-222222222-2-22-2-2-22222-2-22-20000-2200000000-22-2200000000000000
χ252222-2-2222-2-2222-22-22-2-2-2-222-22-2220-20002200-2-200000000000000000000
χ262222-2-2222-2-2222-22-22-2-2-2-222-22-22-202000-2-2002200000000000000000000
χ272222-2-22-2-2222222-2-22-2-222-2-22-2-220000000000000000000000000000002-2
χ282222-2-22-2-2222222-2-22-2-222-2-22-2-22000000000000000000000000000000-22
χ292222-2-22-2-2-2-2222222-2-2-2-2-2-2-2222-2000000000000000000000000002i2i−2i−2i00
χ302222-2-22-2-2-2-2222222-2-2-2-2-2-2-2222-200000000000000000000000000−2i−2i2i2i00
χ312222-2-2-12222-1-1-1-2-22-211-1-1-1-111-1100002-2−i3i3−i3i3i3−i3−i3i3-11-1100000000000000
χ322222-2-2-12222-1-1-1-2-22-211-1-1-1-111-1100002-2i3−i3i3−i3−i3i3i3−i3-11-1100000000000000
χ332222-2-2-12222-1-1-1-2-22-211-1-1-1-111-110000-22−i3i3i3−i3i3−i3i3−i31-11-100000000000000
χ342222-2-2-12222-1-1-1-2-22-211-1-1-1-111-110000-22i3−i3−i3i3−i3i3−i3i31-11-100000000000000
χ352222-2-2-122-2-2-1-1-1-22-221111-1-11-11-120-2000-1-1−i3i311i3−i3−i3i3i3−i300000000000000
χ362222-2-2-122-2-2-1-1-1-22-221111-1-11-11-120-2000-1-1i3−i311−i3i3i3−i3−i3i300000000000000
χ372222-2-2-122-2-2-1-1-1-22-221111-1-11-11-1-20200011−i3i3-1-1i3−i3i3−i3−i3i300000000000000
χ382222-2-2-122-2-2-1-1-1-22-221111-1-11-11-1-20200011i3−i3-1-1−i3i3−i3i3i3−i300000000000000
χ39444444-2-4-444-2-2-2-44-4-4-2-2-2-2222-22200000000000000000000000000000000
χ40444444-2-4-4-4-4-2-2-2-4-444-2-2222222-2-200000000000000000000000000000000
χ414444-4-4-2-4-444-2-2-24-4-4422-2-222-222-200000000000000000000000000000000
χ424444-4-4-2-4-4-4-4-2-2-2444-4222222-2-2-2200000000000000000000000000000000
χ4344-4-40044-4004-4-4000000004-4000000000000000000000000002-22-2000000
χ4444-4-40044-4004-4-4000000004-400000000000000000000000000-22-22000000
χ4544-4-4004-44004-4-400000000-44000000000000000000000000002-2-22000000
χ4644-4-4004-44004-4-400000000-4400000000000000000000000000-222-2000000
χ474-44-44-440000-44-400004-400000000000000000000000000000000002-22-200
χ484-44-44-440000-44-400004-40000000000000000000000000000000000-22-2200
χ494-44-4-4440000-44-40000-4400000000000000000000000000000000002i−2i−2i2i00
χ504-44-4-4440000-44-40000-440000000000000000000000000000000000−2i2i2i−2i00
χ514-4-44004004i−4i-4-440000004i−4i0000000000000000000000002i−2i2-20000000000
χ524-4-44004004i−4i-4-440000004i−4i000000000000000000000000−2i2i-220000000000
χ534-4-4400400−4i4i-4-44000000−4i4i0000000000000000000000002i−2i-220000000000
χ544-4-4400400−4i4i-4-44000000−4i4i000000000000000000000000−2i2i2-20000000000
χ5588-8-800-48-800-44400000000-44000000000000000000000000000000000000
χ5688-8-800-4-8800-444000000004-4000000000000000000000000000000000000
χ578-88-88-8-400004-440000-440000000000000000000000000000000000000000
χ588-88-8-88-400004-4400004-40000000000000000000000000000000000000000
χ598-8-8800-4008i−8i44-4000000−4i4i00000000000000000000000000000000000000
χ608-8-8800-400−8i8i44-40000004i−4i00000000000000000000000000000000000000

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