Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17760 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×#41×C19 ◁ G | |
896 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)(20,21,23,27,24,25,30,32)(22,26,29,33,28,31,34,35)(37,41)(38,44)(39,46)(42,49)(43,47)(48,50);(21,25)(23,30)(26,31)(29,34)(36,37,40,43)(38,42,44,50)(39,47,46,41)(45,49,51,48);(20,22)(21,26)(23,29)(24,28)(25,31)(27,33)(30,34)(32,35)(36,38)(37,42)(39,45)(40,44)(41,48)(43,50)(46,51)(47,49);(22,28)(26,31)(29,34)(33,35)(38,44)(42,50)(45,51)(48,49)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10748);