Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61470 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3482 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
1812 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(23,25)(26,27,31,34)(28,32,30,39)(29,36,38,40)(33,37,41,35);(18,19)(20,23)(21,22)(24,25)(26,28,31,30)(27,32,34,39)(29,37,38,35)(33,36,41,40);(26,29,31,38)(27,33,34,41)(28,35,30,37)(32,40,39,36);(19,22)(23,25)(27,34)(32,39)(33,41)(36,40);(18,20,21,24)(19,23,22,25)(27,34)(32,39)(33,41)(36,40)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54458);