Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24404 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#25949 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C2×C19×#120 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1202 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)(20,21,24,27)(22,26,23,25)(28,29,32,35)(30,36,38,33)(31,34,40,42)(37,41,39,43);(20,22,24,23)(21,25,27,26)(28,30,32,38)(29,33,35,36)(31,39,40,37)(34,41,42,43);(20,22,24,23)(21,26,27,25)(28,31,32,40)(29,34,35,42)(30,37)(33,41)(36,43)(38,39);(20,23,24,22)(21,26,27,25)(29,35)(33,36)(34,42)(41,43)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18937);