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×#21943 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C25×C19 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C24×C4×C19 ◁ G | |
1090 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,30)(27,29)(28,31)(32,33)(34,38)(35,42)(36,45)(37,40)(39,44)(41,46)(43,47);(24,26)(25,28)(27,31)(29,30)(32,34,37,36)(33,38,40,45)(35,41,43,44)(39,42,46,47);(26,31)(28,30)(32,35,36,44,37,43,34,41)(33,39,38,42,40,46,45,47);(25,29)(28,30)(35,43)(39,46)(41,44)(42,47)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14931);