Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#32896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×H(7,𝔽2) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
3610 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)(20,21,26,32)(22,33,36,46)(23,29,38,45)(24,31,25,30)(27,39,43,35)(28,40,44,37)(34,41,51,48)(42,50,47,49);(20,22)(21,27)(23,34)(24,39)(25,35)(26,36)(28,41)(29,42)(30,46)(31,33)(32,43)(37,50)(38,51)(40,49)(44,48)(45,47);(20,23)(21,28)(22,34)(24,37)(25,40)(26,38)(27,41)(29,30)(31,45)(32,44)(33,47)(35,49)(36,51)(39,50)(42,46)(43,48);(20,23)(21,29)(22,34)(24,40)(25,37)(26,38)(27,42)(28,30)(31,44)(32,45)(33,48)(35,50)(36,51)(39,49)(41,46)(43,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25884);