Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11032 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #392 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1438 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,29,26,30,24,31)(22,32,34,27,35,44,41,43)(23,36,38,46,40,28,39,47)(33,48,37,42,50,45,49,51);(20,22)(21,27)(23,37)(24,41)(25,34)(26,35)(28,45)(29,44)(30,43)(31,32)(33,39)(36,48)(38,50)(40,49)(42,46)(47,51);(20,23)(21,28)(22,33)(24,38)(25,39)(26,40)(27,42)(29,46)(30,36)(31,47)(32,45)(34,49)(35,50)(37,41)(43,51)(44,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4020);