Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13099 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1898 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C17×#3008 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C17×H(5,𝔽2) ◁ G | |
666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,28)(20,29)(21,35)(22,27,39,44)(24,31,42,32)(25,38)(26,30)(33,46)(34,47)(36,43)(37,40)(41,48,45,49);(18,20,30,32,23,34,21,31)(19,24,35,47,28,42,26,29)(22,37,38,48,39,33,36,49)(25,40,27,45,43,46,44,41);(18,21,23,30)(19,25,28,43)(20,31,34,32)(22,38,39,36)(24,40,42,46)(26,44,35,27)(29,41,47,45)(33,49,37,48)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6087);