Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#26203 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#2414 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C4×D4×C19 ◁ G | |
844 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,25)(24,27)(28,29)(30,34)(31,32)(33,35)(38,45)(42,50)(46,51)(47,49);(20,22,23,27)(21,24,25,26)(29,32)(33,34)(36,37)(38,46)(39,43)(40,44)(41,48)(42,47)(45,51)(49,50);(28,30,31,35)(29,33,32,34)(36,38,40,45)(37,42,44,50)(39,47,41,49)(43,51,48,46);(21,25)(24,26)(29,32)(33,34)(36,39,40,41)(37,43,44,48)(38,47,45,49)(42,51,50,46)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19191);