Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13100 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1898 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×#41 | C23×C19 |
| prime radical | C2×C19×H(5,𝔽2) | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×C19×H(5,𝔽2) ◁ G | |
672 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)(20,21,25,28,26,31,24,30)(22,32,36,48,37,50,35,49)(23,38,33,46,40,29,41,43)(27,42,44,39,45,51,47,34);(20,22,33,42)(21,27,43,48)(23,39,25,35)(24,36,40,34)(26,37,41,51)(28,44,29,32)(30,47,38,50)(31,45,46,49);(21,28)(23,40)(24,25)(27,44)(29,43)(30,31)(32,48)(34,39)(35,36)(38,46)(45,47)(49,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6088);