Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12741 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#12743 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1786 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#576 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
926 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)(20,21,24,31,26,30,25,42)(22,32,34,48,35,28,41,47)(23,36,38,49,40,43,39,29)(27,37,45,50,44,51,46,33);(20,22)(21,27)(23,37)(24,34)(25,41)(26,35)(28,43)(29,47)(30,44)(31,45)(32,36)(33,39)(38,50)(40,51)(42,46)(48,49);(20,22)(21,28)(23,33)(24,41)(25,34)(26,35)(27,43)(29,46)(30,32)(31,48)(36,44)(37,39)(38,51)(40,50)(42,47)(45,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5731);