Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#22745 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C4×Q8×C19 ◁ G | |
714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(25,29)(30,31)(32,33)(34,41)(35,38)(36,40)(37,44)(39,43)(42,46)(45,47);(24,25,28,29)(26,30,27,31)(34,42)(37,45)(41,46)(44,47);(24,26,28,27)(25,30,29,31)(32,34,43,47,36,42,35,44)(33,37,38,46,40,45,39,41);(24,27,28,26)(25,30,29,31)(32,35,36,43)(33,38,40,39)(34,44,42,47)(37,46,45,41)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15733);