Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21426 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C22×C22⋊C4 |
| prime radical | C2×C19×#121 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C22×C42×C19 ◁ G | |
1132 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)(20,21)(22,25)(23,24)(26,27)(28,29,32,37,33,36,31,35)(30,34,38,41,39,42,40,43);(28,30,32,40,33,39,31,38)(29,34,35,41,36,42,37,43);(21,24)(25,27)(28,31,33,32)(29,35,36,37)(30,38,39,40)(34,41,42,43);(20,22,23,26)(21,25,24,27)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14414);