Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23012 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C4×C4⋊C4×C19 ◁ G | |
982 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25,27,26)(28,29,31,35)(30,37,38,33)(32,34,40,36)(39,42,43,41);(20,22,23,21)(25,26)(28,30,31,38)(29,33,35,37)(32,39,40,43)(34,41,36,42);(29,34)(32,40)(33,41)(35,36)(37,42)(39,43);(24,26,27,25)(29,35)(30,38)(34,36)(39,43)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16000);