Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#32701 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2760 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C19×#534 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C24×C19 ◁ G | |
628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 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)(22,30,33,26)(23,34,37,27)(24,28)(25,29)(31,44)(32,40,46,42)(35,39)(36,47,49,41)(38,43)(45,50)(48,51);(20,22)(21,26)(23,35)(24,32)(25,33)(27,39)(28,42)(29,30)(31,37)(34,44)(36,48)(38,46)(40,43)(41,51)(45,49)(47,50);(20,23)(21,27)(22,31,33,35)(24,36)(25,37)(26,39,30,44)(28,41)(29,34)(32,45,46,48)(38,49)(40,50,42,51)(43,47);(20,24,25,38)(21,28,29,43)(22,32,33,46)(23,36,37,49)(26,40,30,42)(27,41,34,47)(31,45,35,48)(39,50,44,51)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25689);