Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33427 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#117 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C2×#432 |
| prime radical | C24×C19 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C19×#405 ◁ G | |
524 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,28,24,29,36,44,25,26,34,39,37,40,49,51)(22,30,32,46,33,38,48,43,31,45,35,50,47,27,41,42);(21,26)(23,34)(27,38)(29,40)(30,45)(32,35)(36,49)(41,48);(20,22)(21,27,26,38)(23,35)(24,33)(25,31)(28,43,39,42)(29,30,40,45)(32,34)(36,41)(37,47)(44,50,51,46)(48,49);(22,31)(27,38)(30,45)(32,35)(33,47)(41,48)(42,43)(46,50)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26415);