Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34387 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C2×C19×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 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)(25,29)(26,32)(31,36)(33,38)(40,41)(42,45)(43,48)(44,49)(46,50)(47,52)(51,53)(54,55);(25,29)(30,35)(31,36)(37,39)(41,42)(43,50)(47,49)(51,55);(24,25)(26,30)(27,31)(28,29)(32,35)(33,37)(34,36)(38,39)(40,42,45,41)(43,48,50,46)(44,49,52,47)(51,54,55,53);(24,26)(25,30)(27,33)(28,32)(29,35)(31,37)(34,38)(36,39)(40,43)(41,46)(42,48)(44,51)(45,50)(47,53)(49,54)(52,55);(24,27,28,34)(25,31,29,36)(26,33,32,38)(30,37,35,39)(40,44,45,52)(41,47,42,49)(43,51,50,55)(46,53,48,54)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27375);