Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19906 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3358 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(21,25)(23,31)(26,32)(27,34)(28,35)(29,33)(36,37)(38,41)(39,42)(40,44)(43,47)(45,48)(46,50)(49,51);(20,21,24,26)(22,28,30,34)(23,32,31,25)(27,33,35,29)(36,38,40,46)(37,41,44,50)(39,45,47,51)(42,48,43,49);(21,26)(25,32)(27,35)(28,34)(37,42)(39,47)(41,48)(43,44)(45,51)(49,50);(20,22,24,30)(21,27,26,35)(23,33,31,29)(25,34,32,28)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12894);