Finite Group Databasebeta

← Group #11713105

Character table — Group #11713105

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222444466668888888812121212121212121212121212121212121216161616161616161616161624242424242424242424
order12222222444444444444366666664444444444888888881212121212121212121212124444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ4111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111
χ511111111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111
χ711111111-1-1-1-1-1-111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ811111111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ91-11-1-11-11ii−i−i1-1i−i1-1-11111-1-1-11-1i−ii−iii−i−i1-1ii−i−i11-1-111-1-1ii−i−iii−i−i1-1i−i1-1i−i1-1
χ101-11-1-11-11ii−i−i1-1i−i1-1-11111-1-1-11-1i−ii−i−i−iii1-1−i−iii-1-11111-1-1ii−i−iii−i−i-11−ii-11−ii-11
χ111-11-1-11-11ii−i−i-11−ii1-1-11111-1-1-11-1i−i−iiii−i−i-11ii−i−i11-1-1-1-111ii−i−i−i−iii-11−ii1-1−ii-11
χ121-11-1-11-11ii−i−i-11−ii1-1-11111-1-1-11-1i−i−ii−i−iii-11−i−iii-1-111-1-111ii−i−i−i−iii1-1i−i-11i−i1-1
χ131-11-1-11-11−i−iii1-1−ii1-1-11111-1-1-11-1−ii−iiii−i−i1-1ii−i−i-1-11111-1-1−i−iii−i−iii-11i−i-11i−i-11
χ141-11-1-11-11−i−iii1-1−ii1-1-11111-1-1-11-1−ii−ii−i−iii1-1−i−iii11-1-111-1-1−i−iii−i−iii1-1−ii1-1−ii1-1
χ151-11-1-11-11−i−iii-11i−i1-1-11111-1-1-11-1−iii−iii−i−i-11ii−i−i-1-111-1-111−i−iiiii−i−i1-1−ii-11−ii1-1
χ161-11-1-11-11−i−iii-11i−i1-1-11111-1-1-11-1−iii−i−i−iii-11−i−iii11-1-1-1-111−i−iiiii−i−i-11i−i1-1i−i-11
χ1722222222222222222222-1-1-1-1-1-1-1-1222200002200000000-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ18222222222222-2-2-2-22222-1-1-1-1-1-1-1-122-2-20000-2-2000000001111-1-1-1-111110000000000
χ1922222222-2-2-2-222-2-22222-1-1-1-1-1-1-1-1-2-2-2-200002200000000-1-1-1-1111111110000000000
χ2022222222-2-2-2-2-2-2222222-1-1-1-1-1-1-1-1-2-2220000-2-20000000011111111-1-1-1-10000000000
χ212222-2-2-2-20000000022-2-222-222-2-2-200002-22-2002-22-200000000000000000000000000
χ222222-2-2-2-20000000022-2-222-222-2-2-20000-22-2200-22-2200000000000000000000000000
χ232-22-22-22-2000000002-22-222-2-2-22-2200002i−2i−2i2i002i−2i−2i2i00000000000000000000000000
χ242-22-22-22-2000000002-22-222-2-2-22-220000−2i2i2i−2i00−2i2i2i−2i00000000000000000000000000
χ252-22-2-22-222i2i−2i−2i2-22i−2i2-2-22-1-1-1111-112i−2i2i−2i00002-200000000-1-111−i−iii−i−iii0000000000
χ262-22-2-22-222i2i−2i−2i-22−2i2i2-2-22-1-1-1111-112i−2i−2i2i0000-220000000011-1-1−i−iiiii−i−i0000000000
χ272-22-2-22-22−2i−2i2i2i2-2−2i2i2-2-22-1-1-1111-11−2i2i−2i2i00002-200000000-1-111ii−i−iii−i−i0000000000
χ282-22-2-22-22−2i−2i2i2i-222i−2i2-2-22-1-1-1111-11−2i2i2i−2i0000-220000000011-1-1ii−i−i−i−iii0000000000
χ293333333333333333-1-1-1-100000000-1-1-1-11111-1-1-1-1-1-1-1-1-1-1000000000000111111-1-1-1-1
χ303333333333333333-1-1-1-100000000-1-1-1-1-1-1-1-1-1-111111111000000000000-1-1-1-1-1-11111
χ31333333333333-3-3-3-3-1-1-1-100000000-1-111111111-1-1-1-1-1-1-1-1000000000000-1-1-1-1111111
χ32333333333333-3-3-3-3-1-1-1-100000000-1-111-1-1-1-111111111110000000000001111-1-1-1-1-1-1
χ3333333333-3-3-3-333-3-3-1-1-1-10000000011111111-1-1-1-1-1-11111000000000000-1-111-1-1-1-111
χ3433333333-3-3-3-333-3-3-1-1-1-1000000001111-1-1-1-1-1-11111-1-1-1-100000000000011-1-11111-1-1
χ3533333333-3-3-3-3-3-333-1-1-1-10000000011-1-1111111-1-1-1-1111100000000000011-1-1-1-111-1-1
χ3633333333-3-3-3-3-3-333-1-1-1-10000000011-1-1-1-1-1-1111111-1-1-1-1000000000000-1-11111-1-111
χ373-33-3-33-333i3i−3i−3i3-33i−3i-111-100000000−ii−iiii−i−i-11−i−iii-1-1110000000000001-1i−i1-1−ii-11
χ383-33-3-33-333i3i−3i−3i3-33i−3i-111-100000000−ii−ii−i−iii-11ii−i−i11-1-1000000000000-11−ii-11i−i1-1
χ393-33-3-33-333i3i−3i−3i-33−3i3i-111-100000000−iii−iii−i−i1-1−i−iii-1-111000000000000-11−ii1-1i−i1-1
χ403-33-3-33-333i3i−3i−3i-33−3i3i-111-100000000−iii−i−i−iii1-1ii−i−i11-1-10000000000001-1i−i-11−ii-11
χ413-33-3-33-33−3i−3i3i3i3-3−3i3i-111-100000000i−ii−iii−i−i-11−i−iii11-1-1000000000000-11i−i-11−ii1-1
χ423-33-3-33-33−3i−3i3i3i3-3−3i3i-111-100000000i−ii−i−i−iii-11ii−i−i-1-1110000000000001-1−ii1-1i−i-11
χ433-33-3-33-33−3i−3i3i3i-333i−3i-111-100000000i−i−iiii−i−i1-1−i−iii11-1-10000000000001-1−ii-11i−i-11
χ443-33-3-33-33−3i−3i3i3i-333i−3i-111-100000000i−i−ii−i−iii1-1ii−i−i-1-111000000000000-11i−i1-1−ii1-1
χ454444-4-4-4-40000000044-4-4-2-22-2-22220000000000000000000000000000000000000000
χ4644-4-44-4-44000000000000-22-22-2-22200000000000000−2i22i2−2i22i20000000000000000000000
χ4744-4-44-4-44000000000000-22-22-2-222000000000000002i2−2i22i2−2i20000000000000000000000
χ4844-4-4-444-44-44-4000000001-1-1-11-111000000000000000000−i3i3−i3i31-11-1−i3i3−i3i30000000000
χ4944-4-4-444-44-44-4000000001-1-1-11-111000000000000000000i3−i3i3−i31-11-1i3−i3i3−i30000000000
χ5044-4-4-444-44-44-400000000-2222-22-2-20000000000000000000000-22-2200000000000000
χ5144-4-4-444-4-44-44000000001-1-1-11-111000000000000000000−i3i3−i3i3-11-11i3−i3i3−i30000000000
χ5244-4-4-444-4-44-44000000001-1-1-11-111000000000000000000i3−i3i3−i3-11-11−i3i3−i3i30000000000
χ5344-4-4-444-4-44-4400000000-2222-22-2-200000000000000000000002-22-200000000000000
χ544-44-44-44-4000000004-44-4-2-2222-22-20000000000000000000000000000000000000000
χ554-4-4444-4-44i−4i−4i4i000000001-1-11-111-1000000000000000000−i3i3i3−i3i−i−ii3−3−330000000000
χ564-4-4444-4-44i−4i−4i4i000000001-1-11-111-1000000000000000000i3−i3−i3i3i−i−ii−333−30000000000
χ574-4-4444-4-44i−4i−4i4i00000000-222-22-2-220000000000000000000000−2i2i2i−2i00000000000000
χ584-4-4444-4-4−4i4i4i−4i000000001-1-11-111-1000000000000000000−i3i3i3−i3−iii−i−333−30000000000
χ594-4-4444-4-4−4i4i4i−4i000000001-1-11-111-1000000000000000000i3−i3−i3i3−iii−i3−3−330000000000
χ604-4-4444-4-4−4i4i4i−4i00000000-222-22-2-2200000000000000000000002i−2i−2i2i00000000000000
χ614-4-44-4-444000000000000-22-2-2222-200000000000000−2i22i22i2−2i20000000000000000000000
χ624-4-44-4-444000000000000-22-2-2222-2000000000000002i2−2i2−2i22i20000000000000000000000
χ636666-6-6-6-600000000-2-2220000000000002-22-200-22-2200000000000000000000000000
χ646666-6-6-6-600000000-2-222000000000000-22-22002-22-200000000000000000000000000
χ656-66-66-66-600000000-22-220000000000002i−2i−2i2i00−2i2i2i−2i00000000000000000000000000
χ666-66-66-66-600000000-22-22000000000000−2i2i2i−2i002i−2i−2i2i00000000000000000000000000
χ6788-8-88-8-880000000000002-22-222-2-20000000000000000000000000000000000000000
χ688-8-88-8-8880000000000002-222-2-2-220000000000000000000000000000000000000000

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