Finite Group Databasebeta

← Group #10693207

Character table — Group #10693207

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881616161616161616161616162424242424242424242424244848
order122222344666224446688881212121212121212668824242424242424248888242424242424242424444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ91111-1-11-1-11111-111-1-1-1ii−i−i1111-1-1-1-11-1i−iiiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-111-1-1ii−i−ii−i
χ101111-1-11-1-11111-111-1-1-1ii−i−i1111-1-1-1-11-1i−iiiii−i−i−i−i1-1i−i11-1-1ii−i−i-1-111-1-111−i−iii−ii
χ111111-1-11-1-11111-111-1-1-1ii−i−i1111-1-1-1-11-1i−iiiii−i−i−i−i-11−ii-1-111−i−iii11-1-1-1-111ii−i−i−ii
χ121111-1-11-1-11111-111-1-1-1ii−i−i1111-1-1-1-11-1i−iiiii−i−i−i−i-11−ii-1-111−i−iii-1-11111-1-1−i−iiii−i
χ131111-1-11-1-11111-111-1-1-1−i−iii1111-1-1-1-11-1−ii−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-111-1-1−i−iii−ii
χ141111-1-11-1-11111-111-1-1-1−i−iii1111-1-1-1-11-1−ii−i−i−i−iiiii1-1−ii11-1-1−i−iii-1-111-1-111ii−i−ii−i
χ151111-1-11-1-11111-111-1-1-1−i−iii1111-1-1-1-11-1−ii−i−i−i−iiiii-11i−i-1-111ii−i−i11-1-1-1-111−i−iiii−i
χ161111-1-11-1-11111-111-1-1-1−i−iii1111-1-1-1-11-1−ii−i−i−i−iiiii-11i−i-1-111ii−i−i-1-11111-1-1ii−i−i−ii
χ17222222222222-2-22-2-222222222-2-222-2-2-2-2-2-222-2-222-2-200000000000000000000000000
χ18222222222222-2-22-2-222-2-2-2-222-2-222-2-2-2-222-2-222-2-22200000000000000000000000000
χ192222222-2-222222-2-2-2220000-2-2-2-2-2-2-2-2220000000000000000000000000000002i−2i2i−2i00
χ202222222-2-222222-2-2-2220000-2-2-2-2-2-2-2-222000000000000000000000000000000−2i2i−2i2i00
χ212222222-2-2222-2-2-222220000-2-222-2-222-2-200000000000000000000002-22-20000000000
χ222222222-2-2222-2-2-222220000-2-222-2-222-2-20000000000000000000000-22-220000000000
χ23222222-122-1-1-122222-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ24222222-122-1-1-122222-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ25222222-122-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-21111111122-2-2-1-1-1-1111100000000000000
χ26222222-122-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-211111111-2-2221111-1-1-1-100000000000000
χ27222222-122-1-1-1-2-22-2-2-1-12222-1-111-1-11111-2-2-1-111-1-11100003−33−33−33−300000000000000
χ28222222-122-1-1-1-2-22-2-2-1-12222-1-111-1-11111-2-2-1-111-1-1110000−33−33−33−3300000000000000
χ29222222-122-1-1-1-2-22-2-2-1-1-2-2-2-2-1-111-1-111112211-1-111-1-100003−33−3−33−3300000000000000
χ30222222-122-1-1-1-2-22-2-2-1-1-2-2-2-2-1-111-1-111112211-1-111-1-10000−33−333−33−300000000000000
χ312222-2-22222222-2-2-22-2-20000-2-2-2-222222-20000000000000000000000000000002-2-2200
χ322222-2-22222222-2-2-22-2-20000-2-2-2-222222-2000000000000000000000000000000-222-200
χ332222-2-2222222-22-22-2-2-20000-2-22222-2-2-2200000000000000000000002-2-220000000000
χ342222-2-2222222-22-22-2-2-20000-2-22222-2-2-220000000000000000000000-222-20000000000
χ352222-2-22-2-2222-222-22-2-22i2i−2i−2i22-2-2-2-222-22−2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-2-2222-222-22-2-2−2i−2i2i2i22-2-2-2-222-222i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-1-2-2-1-1-12-222-2112i2i−2i−2i-1-1-1-11111-112i−2i−i−i−i−iiiii2-22i−2i-1-111−i−iii00000000000000
χ382222-2-2-1-2-2-1-1-12-222-2112i2i−2i−2i-1-1-1-11111-112i−2i−i−i−i−iiiii-22−2i2i11-1-1ii−i−i00000000000000
χ392222-2-2-1-2-2-1-1-12-222-211−2i−2i2i2i-1-1-1-11111-11−2i2iiiii−i−i−i−i2-2−2i2i-1-111ii−i−i00000000000000
χ402222-2-2-1-2-2-1-1-12-222-211−2i−2i2i2i-1-1-1-11111-11−2i2iiiii−i−i−i−i-222i−2i11-1-1−i−iii00000000000000
χ412222-2-2-1-2-2-1-1-1-222-22112i2i−2i−2i-1-11111-1-11-1−2i2i−i−iiiii−i−i00003−3−33i3−i3−i3i300000000000000
χ422222-2-2-1-2-2-1-1-1-222-22112i2i−2i−2i-1-11111-1-11-1−2i2i−i−iiiii−i−i0000−333−3−i3i3i3−i300000000000000
χ432222-2-2-1-2-2-1-1-1-222-2211−2i−2i2i2i-1-11111-1-11-12i−2iii−i−i−i−iii00003−3−33−i3i3i3−i300000000000000
χ442222-2-2-1-2-2-1-1-1-222-2211−2i−2i2i2i-1-11111-1-11-12i−2iii−i−i−i−iii0000−333−3i3−i3−i3i300000000000000
χ45444444-2-4-4-2-2-244-4-4-4-2-2000022222222-2-2000000000000000000000000000000000000
χ46444444-2-4-4-2-2-2-4-4-444-2-2000022-2-222-2-222000000000000000000000000000000000000
χ474444-4-4-244-2-2-24-4-4-442200002222-2-2-2-2-22000000000000000000000000000000000000
χ484444-4-4-244-2-2-2-44-44-422000022-2-2-2-2222-2000000000000000000000000000000000000
χ4944-4-44-44004-4-4000004-422−2222−2200000000000022−220022−220000000000000000000000000000
χ5044-4-44-44004-4-4000004-4−2222−2222000000000000−222200−22220000000000000000000000000000
χ5144-4-44-4-200-22200000-2222−2222−220023−230023−230000−226−6−226−600000000000000000000000000
χ5244-4-44-4-200-22200000-2222−2222−2200−232300−23230000−22−66−22−6600000000000000000000000000
χ5344-4-44-4-200-22200000-22−2222−22220023−230023−2300002−2−662−2−6600000000000000000000000000
χ5444-4-44-4-200-22200000-22−2222−222200−232300−232300002−26−62−26−600000000000000000000000000
χ5544-4-4-444004-4-400000-44−2i22i22i2−2i2000000000000−2i22i2002i2−2i20000000000000000000000000000
χ5644-4-4-444004-4-400000-442i2−2i2−2i22i20000000000002i2−2i200−2i22i20000000000000000000000000000
χ5744-4-4-44-200-222000002-2−2i22i22i2−2i20023−2300−23230000i2−i2−i6i6−i2i2i6−i600000000000000000000000000
χ5844-4-4-44-200-222000002-2−2i22i22i2−2i200−23230023−230000i2−i2i6−i6−i2i2−i6i600000000000000000000000000
χ5944-4-4-44-200-222000002-22i2−2i2−2i22i20023−2300−23230000−i2i2i6−i6i2−i2−i6i600000000000000000000000000
χ6044-4-4-44-200-222000002-22i2−2i2−2i22i200−23230023−230000−i2i2−i6i6i2−i2i6−i600000000000000000000000000
χ614-4-440044-4-4-440000000000000004-40000000000000000000000000000002-22-2000000
χ624-4-440044-4-4-440000000000000004-4000000000000000000000000000000-22-22000000
χ634-4-44004-44-4-44000000000000000-440000000000000000000000000000002-2-22000000
χ644-4-44004-44-4-44000000000000000-44000000000000000000000000000000-222-2000000
χ658-88-800800-88-8000000000000000000000000000000000000000000000000000000000
χ668-88-800-4004-440000000000043−4300000000000000000000000000000000000000000000
χ678-88-800-4004-4400000000000−434300000000000000000000000000000000000000000000
χ688-8-8800-48-844-4000000000000000-440000000000000000000000000000000000000000
χ698-8-8800-4-8844-40000000000000004-40000000000000000000000000000000000000000

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