Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25196 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1032 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,26,23,21,32,25)(20,27,30,28,31,33,29,24);(18,20,22,30,23,31,32,29)(19,24,26,27,21,28,25,33);(18,21)(19,23)(20,28)(22,26)(24,31)(25,32)(27,30)(29,33);(18,21)(19,23)(20,28)(22,25)(24,31)(26,32)(27,29)(30,33)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18184);