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×#22336 |
| 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 | C19×#392 | C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
806 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)(22,26)(23,25)(24,27)(28,29)(30,33)(31,32)(34,35)(36,37,40,44,39,43,41,47)(38,42,46,50,45,49,48,51);(20,22,23,27)(21,24,25,26)(36,37,41,47,39,43,40,44)(38,42,48,51,45,49,46,50);(22,27)(24,26)(29,32)(33,35)(36,38)(37,42)(39,45)(40,46)(41,48)(43,49)(44,50)(47,51);(21,25)(24,26)(28,30,31,34)(29,33,32,35)(37,43)(38,45)(44,47)(46,48)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15324);