Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17577 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17757 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C42×C19 ◁ G | |
972 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)(20,21,24,27,25,28,23,32)(22,29,30,34,31,26,33,35)(36,37)(38,46)(39,45)(40,43)(41,44)(42,47)(48,51)(49,50);(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,29)(32,35)(36,38)(37,42)(39,47)(40,49)(41,48)(43,46)(44,50)(45,51);(36,39,41,40)(37,43,44,45)(38,47,48,49)(42,46,50,51);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,29,35)(37,44)(42,50)(43,45)(46,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10745);