Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25×C4 |
| direct product | C17×#33559 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C17 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×#41×C17 ◁ G | |
1248 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)(20,24)(21,23)(22,25)(26,32)(27,29)(28,30)(31,33);(19,23)(20,26)(24,31)(25,30)(27,33)(29,32);(20,26)(21,28)(24,32)(29,31);(18,20,22,26)(19,24,25,32)(21,27,28,33)(23,29,30,31)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26547);