Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#12960 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C17 |
| Frattini, cosocle | C22×D4 | C23×C17 |
| prime radical | C2×C17×#120 | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C17 ◁ C22×D4×C17 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23)(24,30)(25,28)(26,29)(27,32)(31,36)(33,35)(34,37);(18,20,21,19)(22,24)(23,27)(25,32)(26,31)(28,30)(29,34)(33,37)(35,36);(24,31)(25,33)(27,34)(30,36)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5948);