Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17780 |
| 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 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×#41×C19 ◁ G | |
870 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)(20,21,24,29,25,28,23,27)(22,30,31,35,32,26,33,34)(37,41)(39,46)(42,48)(43,47)(45,50)(49,51);(20,22)(21,26)(23,31)(24,33)(25,32)(27,34)(28,30)(29,35)(36,37,40,43)(38,42,44,49)(39,47,46,41)(45,51,50,48);(20,23,25,24)(21,27,28,29)(22,31,32,33)(26,34,30,35)(36,38,40,44)(37,42,43,49)(39,45,46,50)(41,48,47,51);(38,44)(42,49)(45,50)(48,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10768);