Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61380 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1734 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)(18,19,22,21)(20,24,25,23)(26,27)(28,32)(29,35)(30,39)(31,34)(33,36)(37,40)(38,41);(18,20,22,25)(19,23,21,24)(26,28)(27,32)(29,38)(30,36)(31,37)(33,39)(34,40)(35,41);(26,28)(27,33)(29,36)(30,38)(31,37)(32,39)(34,41)(35,40);(18,21,22,19)(20,23,25,24)(27,34)(32,40)(33,41)(35,39);(26,29,31,30)(27,35,34,39)(28,36,37,38)(32,33,40,41)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54368);