Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C22×C42×C19 ◁ G | |
1182 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
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)(21,23)(24,25)(26,29)(27,28)(30,31)(32,33,37,39,36,40,35,41)(34,42,43,38,45,47,44,46);(20,21,22,23)(32,34)(33,38)(35,43)(36,45)(37,44)(39,42)(40,46)(41,47);(25,28)(29,31)(32,35,36,37)(33,39,40,41)(34,43,45,44)(38,42,46,47);(24,26,27,30)(25,29,28,31)(33,40)(38,46)(39,41)(42,47)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14384);