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×#17761 |
| 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)(22,29)(23,25)(24,28)(26,30)(27,32)(31,34)(33,35)(36,37,40,45,41,43,39,44)(38,46,48,42,49,51,47,50);(21,25)(23,32)(26,33)(27,28)(29,34)(31,35)(36,38,41,49)(37,42,43,50)(39,48,40,47)(44,51,45,46);(20,22)(21,26)(23,31)(24,30)(25,33)(27,34)(28,29)(32,35)(37,43)(42,50)(44,45)(46,51);(22,30)(26,29)(31,35)(33,34)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10749);