Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11203 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×C22⋊C4 |
| commutator | C24 | C22×C4×C17 |
| Frattini, cosocle | C25 | C23×C17 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C24×C4×C17 ◁ G | |
1194 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(26,27)(28,32,33,30)(29,31);(18,19,21,20)(22,23)(24,25);(18,20,21,19)(23,25)(26,28)(27,30)(29,33)(31,32)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4191);