Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61499 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3522 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#529 ◁ G | |
1806 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)(26,27,32,36)(28,33,29,38)(30,35,31,40)(34,37,41,39);(18,19)(20,23)(21,22)(24,25)(26,28)(27,33)(29,32)(30,39)(31,37)(34,35)(36,38)(40,41);(26,29,32,28)(27,34,36,41)(30,39,31,37)(33,40,38,35);(19,22)(23,25);(18,20,21,24)(19,23,22,25)(26,30,32,31)(27,35,36,40)(28,37,29,39)(33,41,38,34)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54487);