Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33689 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#575 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C4×M16×C19 ◁ G | |
520 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)(20,21,25,29)(22,30,32,48)(23,35,36,51)(24,40,38,28)(26,41,43,33)(27,45,46,39)(31,47,34,50)(37,42,49,44);(23,36)(27,46)(30,48)(33,41)(35,51)(37,49)(39,45)(47,50);(20,22)(21,26)(23,37)(24,31)(25,32)(27,47)(28,42)(29,43)(30,35)(33,39)(34,38)(36,49)(40,44)(41,45)(46,50)(48,51);(22,31,32,34)(23,36)(26,42,43,44)(27,46)(30,47,48,50)(33,37,41,49)(35,51)(39,45)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26677);