Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C29 |
| direct product | C19×#20609 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| prime radical | C22×C19×H(5,𝔽2) | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C25×C19 ◁ G | |
4122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25)(26,32,34,29)(27,30)(28,31)(33,36,39,38)(35,37);(24,26)(25,29)(27,33)(28,34)(30,36)(31,32)(35,39)(37,38);(21,23)(24,27)(25,30)(26,33)(28,35)(29,36)(31,37)(32,38)(34,39);(25,31)(29,32)(30,37)(36,38)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13597);