Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10518 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#10520 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
440 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)(18,19)(20,23)(21,24)(22,25)(26,27,30,32)(28,33,31,29);(18,19)(20,24)(21,23)(22,25)(27,28)(29,33)(31,32);(19,23)(20,21)(24,25)(26,28,29,27,30,31,33,32)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3508);