Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23551 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C22×D4 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C22×C42×C19 ◁ G | |
1154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
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)(24,25,28,30)(26,31,27,29)(32,33)(34,41)(35,39)(36,44)(37,40)(38,42)(43,46)(45,47);(20,21)(22,23)(24,26,28,27)(25,29,30,31);(21,23)(24,27,28,26)(25,29,30,31)(32,34)(33,38)(35,42)(36,45)(37,43)(39,46)(40,47)(41,44);(32,35,37,36)(33,39,40,44)(34,42,43,45)(38,46,47,41)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16539);