Finite Group Databasebeta

← Group #10692452

Character table — Group #10692452

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881616161616161616161616162424242424242424242424244848
order12222234466644444668888121212121212121288121224242424242424248888242424242424242424444444888844
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
χ51111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ91111-1-11-1-111111-11-1-1-1ii−i−i11-111-1-1-1i−i1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-11-1-11ii−i−ii−ii−i1-1
χ101111-1-11-1-111111-11-1-1-1ii−i−i11-111-1-1-1i−i1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-1-111-1−i−iii−ii−ii-11
χ111111-1-11-1-111111-11-1-1-1ii−i−i11-111-1-1-1i−i1-1iiii−i−i−i−i−ii-11−i−iii-1-1111-1-11−i−iiii−ii−i-11
χ121111-1-11-1-111111-11-1-1-1ii−i−i11-111-1-1-1i−i1-1iiii−i−i−i−i−ii-11−i−iii-1-111-111-1ii−i−i−ii−ii1-1
χ131111-1-11-1-111111-11-1-1-1−i−iii11-111-1-1-1−ii1-1−i−i−i−iiiiii−i-11ii−i−i-1-1111-1-11ii−i−i−ii−ii-11
χ141111-1-11-1-111111-11-1-1-1−i−iii11-111-1-1-1−ii1-1−i−i−i−iiiiii−i-11ii−i−i-1-111-111-1−i−iiii−ii−i1-1
χ151111-1-11-1-111111-11-1-1-1−i−iii11-111-1-1-1−ii1-1−i−i−i−iiiii−ii1-1−i−iii11-1-11-1-11−i−iii−ii−ii1-1
χ161111-1-11-1-111111-11-1-1-1−i−iii11-111-1-1-1−ii1-1−i−i−i−iiiii−ii1-1−i−iii11-1-1-111-1ii−i−ii−ii−i-11
χ172222222222222-2-2-2-2222222222-2-2-2-22-2-2-2-222-2-222-2-200000000000000000000000000
χ182222222222222-2-2-2-222-2-2-2-2222-2-2-2-2222-2-2-2-222-2-22200000000000000000000000000
χ192222222-2-2222-222-2-2220000-2-2-2-2-2-2-2-2002200000000000000000000000000002i−2i−2i2i00
χ202222222-2-2222-222-2-2220000-2-2-2-2-2-2-2-200220000000000000000000000000000−2i2i2i−2i00
χ212222222-2-2222-2-2-222220000-2-2-22222-200-2-20000000000000000000022-2-20000000000
χ222222222-2-2222-2-2-222220000-2-2-22222-200-2-200000000000000000000-2-2220000000000
χ23222222-122-1-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ24222222-122-1-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ25222222-122-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ26222222-122-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ27222222-122-1-1-12-2-2-2-2-1-12222-1-1-11111-1-2-211-1-111-1-11100003−33−33−33−300000000000000
χ28222222-122-1-1-12-2-2-2-2-1-12222-1-1-11111-1-2-211-1-111-1-1110000−33−33−33−3300000000000000
χ29222222-122-1-1-12-2-2-2-2-1-1-2-2-2-2-1-1-11111-1221111-1-111-1-100003−33−3−33−3300000000000000
χ30222222-122-1-1-12-2-2-2-2-1-1-2-2-2-2-1-1-11111-1221111-1-111-1-10000−33−333−33−300000000000000
χ312222-2-2222222-22-2-22-2-20000-2-22-2-2222002-2000000000000000000000000000022-2-200
χ322222-2-2222222-22-2-22-2-20000-2-22-2-2222002-20000000000000000000000000000-2-22200
χ332222-2-2222222-2-222-2-2-20000-2-2222-2-2200-22000000000000000000002-22-20000000000
χ342222-2-2222222-2-222-2-2-20000-2-2222-2-2200-2200000000000000000000-22-220000000000
χ352222-2-22-2-22222-22-22-2-22i2i−2i−2i22-2-2-222-2−2i2i-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-2-22222-22-22-2-2−2i−2i2i2i22-2-2-222-22i−2i-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-1-2-2-1-1-122-22-2112i2i−2i−2i-1-11-1-11112i−2i-11−i−i−i−iiiii2i−2i2-2−i−iii-1-11100000000000000
χ382222-2-2-1-2-2-1-1-122-22-2112i2i−2i−2i-1-11-1-11112i−2i-11−i−i−i−iiiii−2i2i-22ii−i−i11-1-100000000000000
χ392222-2-2-1-2-2-1-1-122-22-211−2i−2i2i2i-1-11-1-1111−2i2i-11iiii−i−i−i−i2i−2i-22−i−iii11-1-100000000000000
χ402222-2-2-1-2-2-1-1-122-22-211−2i−2i2i2i-1-11-1-1111−2i2i-11iiii−i−i−i−i−2i2i2-2ii−i−i-1-11100000000000000
χ412222-2-2-1-2-2-1-1-12-22-22112i2i−2i−2i-1-1111-1-11−2i2i1-1−i−iiiii−i−i0000−i3i3i3−i3−333−300000000000000
χ422222-2-2-1-2-2-1-1-12-22-22112i2i−2i−2i-1-1111-1-11−2i2i1-1−i−iiiii−i−i0000i3−i3−i3i33−3−3300000000000000
χ432222-2-2-1-2-2-1-1-12-22-2211−2i−2i2i2i-1-1111-1-112i−2i1-1ii−i−i−i−iii0000−i3i3i3−i33−3−3300000000000000
χ442222-2-2-1-2-2-1-1-12-22-2211−2i−2i2i2i-1-1111-1-112i−2i1-1ii−i−i−i−iii0000i3−i3−i3i3−333−300000000000000
χ45444444-2-4-4-2-2-2-444-4-4-2-200002222222200-2-20000000000000000000000000000000000
χ46444444-2-4-4-2-2-2-4-4-444-2-20000222-2-2-2-2200220000000000000000000000000000000000
χ474444-4-4-244-2-2-2-44-4-4422000022-222-2-2-200-220000000000000000000000000000000000
χ484444-4-4-244-2-2-2-4-444-422000022-2-2-222-2002-20000000000000000000000000000000000
χ4944-4-40044-44-4-4000000000000040000-400000000000000000000000000002-22-2000000
χ5044-4-40044-44-4-4000000000000040000-40000000000000000000000000000-22-22000000
χ5144-4-4004-444-4-40000000000000-40000400000000000000000000000000002i−2i−2i2i000000
χ5244-4-4004-444-4-40000000000000-4000040000000000000000000000000000−2i2i2i−2i000000
χ534-44-44-4400-44-4000004-422−2222−2200000000000022−220022−220000000000000000000000000000
χ544-44-44-4400-44-4000004-4−2222−2222000000000000−222200−22220000000000000000000000000000
χ554-44-44-4-2002-2200000-2222−2222−2200023−2323−2300000−226−6−226−600000000000000000000000000
χ564-44-44-4-2002-2200000-2222−2222−22000−2323−232300000−22−66−22−6600000000000000000000000000
χ574-44-44-4-2002-2200000-22−2222−222200023−2323−23000002−2−662−2−6600000000000000000000000000
χ584-44-44-4-2002-2200000-22−2222−2222000−2323−2323000002−26−62−26−600000000000000000000000000
χ594-44-4-44400-44-400000-44−2i22i22i2−2i2000000000000−2i22i2002i2−2i20000000000000000000000000000
χ604-44-4-44400-44-400000-442i2−2i2−2i22i20000000000002i2−2i200−2i22i20000000000000000000000000000
χ614-44-4-44-2002-22000002-2−2i22i22i2−2i200023−23−232300000i2−i2−i6i6−i2i2i6−i600000000000000000000000000
χ624-44-4-44-2002-22000002-2−2i22i22i2−2i2000−232323−2300000i2−i2i6−i6−i2i2−i6i600000000000000000000000000
χ634-44-4-44-2002-22000002-22i2−2i2−2i22i200023−23−232300000−i2i2i6−i6i2−i2−i6i600000000000000000000000000
χ644-44-4-44-2002-22000002-22i2−2i2−2i22i2000−232323−2300000−i2i2−i6i6i2−i2i6−i600000000000000000000000000
χ6588-8-800-48-8-4440000000000000-40000400000000000000000000000000000000000000
χ6688-8-800-4-88-444000000000000040000-400000000000000000000000000000000000000
χ678-8-8800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-8800-40044-40000000000043−4300000000000000000000000000000000000000000000
χ698-8-8800-40044-400000000000−434300000000000000000000000000000000000000000000

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