Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#22898 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | D42 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | #2358 |
| prime radical | C19×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ G | |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(20,21,24,30,25,31,40,29)(22,28,34,43,35,42,33,26)(23,36,37,46,39,45,38,27)(32,47,49,51,50,41,48,44);(20,22,24,34,25,35,40,33)(21,26,30,28,31,43,29,42)(23,32,37,49,39,50,38,48)(27,41,36,44,46,47,45,51);(20,23)(21,27)(22,32)(24,37)(25,39)(26,41)(28,44)(29,45)(30,36)(31,46)(33,48)(34,49)(35,50)(38,40)(42,51)(43,47);(20,22)(21,28)(23,32)(24,34)(25,35)(26,29)(27,44)(30,43)(31,42)(33,40)(36,47)(37,49)(38,48)(39,50)(41,45)(46,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15886);