Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13318 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13318 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,33)(23,37)(24,32)(25,30)(26,31)(27,34)(28,35)(29,41)(36,49)(38,50)(39,45)(40,46)(42,48)(43,47)(44,51);(20,22)(21,27)(23,38)(24,35)(25,43)(26,36)(28,46)(29,47)(30,44)(31,45)(32,50)(33,37)(34,41)(39,40)(42,51)(48,49);(20,22)(21,28)(23,39)(24,43)(25,35)(26,36)(27,29)(30,49)(31,47)(32,33)(34,42)(37,44)(38,40)(41,51)(45,46)(48,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6306);