Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34247 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C25×C19 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(25,29)(30,31)(32,33)(34,40)(35,43)(36,37)(38,42)(39,44)(41,45)(46,47);(20,22,23,21)(33,37)(38,40)(39,43)(45,46);(24,25)(26,30)(27,31)(28,29)(32,34,36,42)(33,38,37,40)(35,41,44,47)(39,45,43,46);(24,26,28,27)(25,30,29,31)(32,33)(34,38)(35,39)(36,37)(40,42)(41,45)(43,44)(46,47);(24,27,28,26)(25,31,29,30)(32,35)(33,39)(34,41)(36,44)(37,43)(38,45)(40,46)(42,47)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27235);