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 |
| direct product | C17×#22539 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#127 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×Q8×C17 ◁ G | |
1066 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(24,25)(26,27,30,35,31,34,28,32)(29,37,36,41,38,33,39,40);(18,19,22,23)(20,24,21,25)(26,28,31,30)(27,32,34,35)(29,36,38,39)(33,40,37,41);(18,20,22,21)(19,24,23,25)(26,29,31,38)(27,33,34,37)(28,36,30,39)(32,40,35,41);(18,21,22,20)(19,24,23,25)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15527);