Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13339 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,31,37)(26,38,43,73)(27,44,50,63)(28,51,56,69)(29,36,30,35)(32,57,61,40)(33,46,66,47)(34,54,70,55)(39,58,77,86)(41,67,42,72)(45,82,76,62)(48,68,49,81)(52,59,79,60)(53,64,84,65)(71,74,87,75)(78,80,83,85);(20,21)(22,23)(24,26,31,43)(25,32,37,61)(27,45,50,76)(28,52,56,79)(29,42,30,41)(33,62,66,82)(34,67,70,72)(35,60,36,59)(38,69,73,51)(39,49,77,48)(40,54,57,55)(44,80,63,85)(46,74,47,75)(53,83,84,78)(58,65,86,64)(68,87,81,71);(21,23)(24,27)(25,33)(26,39)(28,53)(29,49)(30,48)(31,50)(32,58)(34,68)(35,65)(36,64)(37,66)(38,71)(40,78)(41,76)(42,45)(43,77)(44,51)(46,54)(47,55)(52,75)(56,84)(57,83)(59,82)(60,62)(61,86)(63,69)(67,80)(70,81)(72,85)(73,87)(74,79)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6327);