Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25×C4 |
| direct product | C17×#22406 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| prime radical | C2×C17×#547 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4⋊C4×C17 ◁ G | |
1474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23)(24,28)(25,33,35,29)(26,30)(27,31)(32,37,34,36);(18,19)(20,21)(22,24,27,26)(23,28,31,30)(25,32,35,34)(29,36,33,37);(22,25)(23,29)(24,32)(26,34)(27,35)(28,36)(30,37)(31,33);(19,21)(22,26,27,24)(23,30,31,28)(25,34,35,32)(29,37,33,36)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15394);