Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#8196 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C19 | C2×D4 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | C4×C22⋊C4 |
| prime radical | C2×#41×C19 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1216 |
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)(22,24)(23,26)(25,27)(28,29,32,30,31,33,35,34);(21,24,26,25)(29,33)(30,34);(28,30,32,33,31,34,35,29)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1184);