Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#10735 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C25 | C23×C19 |
| prime radical | C26×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C26×C19 ◁ G | |
3062 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 35 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)(26,27)(28,29)(30,32,34,35)(31,33);(21,23)(28,30)(29,32,33,35)(31,34);(25,27)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3723);