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×#13103 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1898 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C17×#3010 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C17×2−1+4 ◁ G | |
646 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)(18,19,24,29,25,30,23,28)(20,22,27,40,33,41,42,31)(21,34,37,26,38,44,36,45)(32,47,43,35,48,49,46,39);(18,20,31,19)(21,32,47,26)(22,29,23,42)(24,27,41,28)(25,33,40,30)(34,37,43,39)(35,44,36,46)(38,48,49,45);(18,21,25,38)(19,26,30,45)(20,32,33,48)(22,39,41,35)(23,37,24,36)(27,46,42,43)(28,44,29,34)(31,47,40,49)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6091);