Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#22360 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C23×C4 |
| prime radical | C22×D4×C19 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
710 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(21,24)(22,26)(28,29)(30,34)(31,33)(32,35)(36,37,41,38,40,43,50,45)(39,46,49,47,48,42,51,44);(20,21)(22,25)(23,24)(26,27)(28,30)(29,32)(31,35)(33,34)(36,38,41,43,40,45,50,37)(39,47,49,42,48,44,51,46);(21,24)(25,27)(29,33)(30,35)(36,39)(37,42)(38,44)(40,48)(41,49)(43,46)(45,47)(50,51);(20,22,23,26)(21,25,24,27)(29,33)(32,34)(37,43)(38,45)(39,48)(49,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15348);