Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21824 |
| 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 | C24×C19 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
1006 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25)(26,32)(27,30)(28,31)(29,34)(33,38)(35,37)(36,39)(40,41,43,46,44,47,50,53)(42,45,49,52,48,51,54,55);(24,26,28,34)(25,29,31,32)(27,35,36,33)(30,38,39,37)(40,42)(41,45)(43,49)(44,48)(46,52)(47,51)(50,54)(53,55);(21,23)(24,27,28,36)(25,30,31,39)(26,33,34,35)(29,37,32,38);(25,31)(29,32)(30,39)(37,38)(42,48)(45,51)(49,54)(52,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14812);