Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12948 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1864 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
384 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)(21,27,30,29)(22,32,33,50)(23,35)(24,39)(25,38)(28,45)(31,40,42,36)(34,41,43,37)(44,51)(46,48);(20,21,25,42,26,30,38,31)(22,28,43,47,33,45,34,49)(23,36,35,27,24,40,39,29)(32,44,41,51,50,48,37,46);(20,22)(21,28)(23,37)(24,41)(25,43)(26,33)(27,44)(29,48)(30,45)(31,49)(32,35)(34,38)(36,46)(39,50)(40,51)(42,47)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5936);