Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20936 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C23×D4×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
1850 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
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)(21,23)(24,25)(26,27)(28,29,33,37,34,30,32,36)(31,39,41,35,42,43,40,38);(20,21,22,23)(28,30,34,29)(31,38,42,35)(32,36,33,37)(39,41,43,40);(25,27)(28,31,34,42)(29,35,30,38)(32,41,33,40)(36,43,37,39);(29,30)(35,38)(36,37)(39,43)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13924);