Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24421 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(20,21,26,40,25,27,24,30)(22,31,39,28,34,42,32,41)(23,35,37,44,38,29,36,45)(33,46,47,50,48,51,49,43);(21,27)(22,32)(24,26)(28,42)(29,35)(31,41)(33,47)(34,39)(36,37)(43,51)(46,50)(48,49);(20,22)(21,28)(23,33)(24,39)(25,34)(26,32)(27,41)(29,43)(30,42)(31,40)(35,50)(36,47)(37,49)(38,48)(44,46)(45,51);(20,23)(21,29)(22,33)(24,37)(25,38)(26,36)(27,35)(28,43)(30,45)(31,46)(32,47)(34,48)(39,49)(40,44)(41,50)(42,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17409);