Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#22388 |
| 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 | |
726 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)(20,21)(22,25)(23,26)(24,27)(28,29)(30,33)(31,32)(34,35)(36,37,40,44,39,43,41,48)(38,45,47,51,46,42,49,50);(20,22,25,21)(23,26,24,27)(36,37,41,48,39,43,40,44)(38,45,49,50,46,42,47,51);(20,23,25,24)(21,26,22,27)(29,32)(33,35)(36,38,39,46)(37,42,43,45)(40,47,41,49)(44,50,48,51);(20,24,25,23)(21,26,22,27)(28,30,31,34)(29,33,32,35)(37,43)(38,46)(44,48)(47,49)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15376);