Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18107 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×#120 |
| prime radical | C19×#3459 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
1000 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(22,29)(23,27)(24,32)(25,28)(26,30)(31,34)(33,35)(36,37,40,43)(38,41,45,48)(39,42,46,49)(44,50,51,47);(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32)(36,38)(37,41)(39,44)(40,45)(42,47)(43,48)(46,51)(49,50);(36,39)(37,42)(38,44)(40,46)(41,47)(43,49)(45,51)(48,50);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11095);