Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33638 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33638 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#476 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
514 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)(21,27)(22,32,34,50)(23,25)(24,36)(28,42,43,46)(29,31)(33,37,39,49)(35,38)(40,44,48,51)(41,47);(20,21,23,27,26,29,25,31)(22,28,33,40,34,43,39,48)(24,30,35,41,38,45,36,47)(32,44,49,42,50,51,37,46);(20,22)(21,28)(23,33)(24,37)(25,39)(26,34)(27,40)(29,43)(30,46)(31,48)(32,35)(36,50)(38,49)(41,44)(42,45)(47,51);(21,29)(27,31)(28,43)(30,45)(40,48)(41,47)(42,46)(44,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26626);