Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34348 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| socle | C23×C19 | C25 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
1898 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)(24,25)(26,32)(27,31)(28,30)(29,33)(34,38)(35,37)(36,39)(40,41)(42,45)(43,50)(44,47)(46,52)(48,55)(49,54)(51,53);(24,26)(25,29)(27,34)(28,33)(30,32)(31,36)(35,39)(37,38)(40,42,44,49)(41,45,47,54)(43,51,52,48)(46,55,50,53);(26,33)(29,32)(34,39)(36,38)(40,43,44,52)(41,46,47,50)(42,48,49,51)(45,53,54,55);(25,30)(26,33)(31,37)(34,39)(41,47)(45,54)(46,50)(53,55);(24,27,28,35)(25,31,30,37)(26,34,33,39)(29,36,32,38)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27336);