Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#22588 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C19×C22⋊C8 ◁ G | |
888 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)(22,24)(23,25)(26,27)(28,29,32,36,33,30,37,35)(31,34,42,43,40,38,41,39);(20,22,23,26)(21,24,25,27)(28,30)(29,33)(31,39)(32,35)(34,42)(36,37)(38,41)(40,43);(21,25)(24,27)(31,40)(34,38)(39,43)(41,42);(28,31)(29,34)(30,38)(32,42)(33,40)(35,39)(36,43)(37,41)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15576);