Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#26855 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#2002 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
764 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,27)(23,25)(24,26)(28,29)(30,31)(32,38)(33,37)(34,39)(35,36)(40,42)(41,43);(20,22,24,23)(21,25,26,27)(28,29,33,38,34,39,32,37)(30,31,36,42,41,43,40,35);(20,23,24,22)(21,25,26,27)(28,30,32,40,34,41,33,36)(29,35,37,43,39,42,38,31);(21,26)(25,27)(28,31,32,35,34,43,33,42)(29,36,37,30,39,40,38,41)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19843);