Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18406 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3506 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
998 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)(20,21,25,29)(22,30,33,34)(23,27,24,28)(26,32,35,31)(39,46)(41,47)(42,49)(44,50);(20,22)(21,26)(23,31)(24,32)(25,33)(27,34)(28,30)(29,35)(36,37)(38,41)(39,42)(40,43)(44,48)(45,47)(46,49)(50,51);(20,23,25,24)(21,27,29,28)(22,31,33,32)(26,34,35,30)(36,38,40,45)(37,41,43,47)(39,44,46,50)(42,48,49,51);(20,23,25,24)(21,28,29,27)(22,32,33,31)(26,34,35,30)(36,39,40,46)(37,42,43,49)(38,44,45,50)(41,48,47,51)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11394);