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×#17768 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3511 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×#41×C19 ◁ G | |
918 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)(36,37)(38,45)(39,42)(40,44)(41,49)(43,47)(46,50)(48,51);(21,25)(23,30)(26,31)(29,34)(36,38)(37,43)(39,46)(40,47)(41,50)(42,48)(44,51)(45,49);(20,22,24,28)(21,26,25,31)(23,29,30,34)(27,33,32,35)(36,39,42,37)(38,46,48,43)(40,44,41,49)(45,47,51,50);(22,28)(26,31)(29,34)(33,35)(36,40,42,41)(37,44,39,49)(38,47,48,50)(43,51,46,45)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10756);