Finite Group Databasebeta

← Group #10714547

Character table — Group #10714547

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12222234444666668888121212122424242416161616242448484848484848482444661212121212124488161616162444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ92222222222222222-2-2-2-22222-2-2-2-20000-2-20000000000000000000022-2-200000000
χ102222222222222222-2-2-2-22222-2-2-2-20000-2-200000000000000000000-2-22200000000
χ112222222-2-2-2-2222220000-2-2-2-2000022−2−2002222−2−2−2−20000000000002-20022−2−20000
χ122222222-2-2-2-2222220000-2-2-2-2000022−2−2002222−2−2−2−2000000000000-2200−2−2220000
χ132222222-2-2-2-2222220000-2-2-2-20000−2−22200−2−2−2−222220000000000002-200−2−2220000
χ142222222-2-2-2-2222220000-2-2-2-20000−2−22200−2−2−2−22222000000000000-220022−2−20000
χ15222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ18222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ192222-2-22-2-222222-2-22-22-22-2-2222220000-2-200000000000000000000000000002-200
χ202222-2-22-2-222222-2-22-22-22-2-2222220000-2-20000000000000000000000000000-2200
χ212222-2-22-2-222222-2-2-22-222-2-22-2-2-2-2000022000000002-20022-2-20000000000000000
χ222222-2-22-2-222222-2-2-22-222-2-22-2-2-2-200002200000000-2200-2-2220000000000000000
χ232222-2-2-1-2-222-1-1-111-22-22-111-111110000-1-133−3−333−3−32-200-1-11133−3−3000000000000
χ242222-2-2-1-2-222-1-1-111-22-22-111-111110000-1-133−3−333−3−3-220011-1-1−3−333000000000000
χ252222-2-2-1-2-222-1-1-111-22-22-111-111110000-1-1−3−333−3−3332-200-1-111−3−333000000000000
χ262222-2-2-1-2-222-1-1-111-22-22-111-111110000-1-1−3−333−3−333-220011-1-133−3−3000000000000
χ272-22-22-222-22-2-2-222-22-2-22-22-2222-2-22i−2i2i−2i2-22i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ282-22-22-222-22-2-2-222-22-2-22-22-2222-2-2−2i2i−2i2i2-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ292-22-22-222-22-2-2-222-2-222-2-22-22-2-2220000-220000000000000000000000002i−2i2i−2i0000
χ302-22-22-222-22-2-2-222-2-222-2-22-22-2-2220000-22000000000000000000000000−2i2i−2i2i0000
χ312-22-22-22-22-22-2-222-200002-22-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2000000000000002-2−i2i2i2−i20000
χ322-22-22-22-22-22-2-222-200002-22-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200000000000000-22i2−i2−i2i20000
χ332-22-22-22-22-22-2-222-200002-22-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2000000000000002-2i2−i2−i2i20000
χ342-22-22-22-22-22-2-222-200002-22-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200000000000000-22−i2i2i2−i20000
χ352-22-22-2-12-22-211-1-112-2-221-11-1-1-1112i−2i2i−2i-11−ii−ii−ii−ii0000−i3i3−i3i33−33−3000000000000
χ362-22-22-2-12-22-211-1-112-2-221-11-1-1-1112i−2i2i−2i-11−ii−ii−ii−ii0000i3−i3i3−i3−33−33000000000000
χ372-22-22-2-12-22-211-1-112-2-221-11-1-1-111−2i2i−2i2i-11i−ii−ii−ii−i0000−i3i3−i3i3−33−33000000000000
χ382-22-22-2-12-22-211-1-112-2-221-11-1-1-111−2i2i−2i2i-11i−ii−ii−ii−i0000i3−i3i3−i33−33−3000000000000
χ392-22-2-222-222-2-2-22-2222-2-2-2-22222-2-20000-220000000000000000000000000000002i−2i
χ402-22-2-222-222-2-2-22-2222-2-2-2-22222-2-20000-22000000000000000000000000000000−2i2i
χ412-22-2-222-222-2-2-22-22-2-222-2-222-2-22200002-200000000002-200002-2-22000000000000
χ422-22-2-222-222-2-2-22-22-2-222-2-222-2-22200002-20000000000-220000-222-2000000000000
χ432-22-2-22-1-222-211-11-1-2-22211-1-111-1-10000-11−i3i3i3−i3−i3i3i3−i3002-2−i3i3i3−i3-111-1000000000000
χ442-22-2-22-1-222-211-11-1-2-22211-1-111-1-10000-11−i3i3i3−i3−i3i3i3−i300-22i3−i3−i3i31-1-11000000000000
χ452-22-2-22-1-222-211-11-1-2-22211-1-111-1-10000-11i3−i3−i3i3i3−i3−i3i3002-2i3−i3−i3i3-111-1000000000000
χ462-22-2-22-1-222-211-11-1-2-22211-1-111-1-10000-11i3−i3−i3i3i3−i3−i3i300-22−i3i3i3−i31-1-11000000000000
χ47444444-24444-2-2-2-2-2-4-4-4-4-2-2-2-2222200002200000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-2-2-20000222200002222−22−2200−2−2−2−22222000000000000000000000000
χ49444444-2-4-4-4-4-2-2-2-2-2000022220000−22−222222002222−2−2−2−2000000000000000000000000
χ504444-4-4444-4-4444-4-40000-444-4000000000000000000000000000000000000000000
χ514444-4-4-244-4-4-2-2-22200002-2-22000000000066−6−6−6−666000000000000000000000000
χ524444-4-4-244-4-4-2-2-22200002-2-220000000000−6−66666−6−6000000000000000000000000
χ534444-4-4-2-4-444-2-2-2224-44-4-222-2-2-2-2-200002200000000000000000000000000000000
χ544-44-44-4-24-44-422-2-22-444-42-22-222-2-200002-200000000000000000000000000000000
χ554-44-44-4-2-44-4422-2-220000-22-220000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ564-44-44-4-2-44-4422-2-220000-22-2200002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ574-44-4-4444-4-44-4-44-44000044-4-4000000000000000000000000000000000000000000
χ584-44-4-44-24-4-4422-22-20000-2-2220000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ594-44-4-44-24-4-4422-22-20000-2-2220000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ604-44-4-44-2-444-422-22-244-4-422-2-2-2-22200002-200000000000000000000000000000000
χ6188-8-800800008-8-80000000000000000000000000000000000000000000000000000
χ6288-8-800-40000-444000000000026−2626−2600000000000000000000000000000000000000
χ6388-8-800-40000-4440000000000−2626−262600000000000000000000000000000000000000
χ648-8-880080000-88-80000000000000000000000000000000000000000000000000000
χ658-8-8800-400004-44000000000026−26−262600000000000000000000000000000000000000
χ668-8-8800-400004-440000000000−262626−2600000000000000000000000000000000000000

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