Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#8325 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C2×C19×#121 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
748 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 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)(22,29,31,26)(23,25)(24,28)(27,32)(30,34,35,33)(36,37,39,42,40,43,46,49)(38,41,45,48,44,47,50,51);(21,25)(23,32)(26,33)(27,28)(29,34)(30,35)(36,38)(37,41)(39,45)(40,44)(42,48)(43,47)(46,50)(49,51);(20,22)(21,26)(23,30)(24,31)(25,33)(27,34)(28,29)(32,35)(38,44)(41,47)(45,50)(48,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1313);