Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#25196 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1032 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,28,25,23,34,27)(22,29,32,30,33,35,31,26);(20,22,24,32,25,33,34,31)(21,26,28,29,23,30,27,35);(20,23)(21,25)(22,30)(24,28)(26,33)(27,34)(29,32)(31,35);(20,23)(21,25)(22,30)(24,27)(26,33)(28,34)(29,31)(32,35)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18184);