Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#13156 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1936 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
306 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)(19,25,29,36)(20,31,34,39)(21,26)(22,37)(23,40)(27,42)(28,45,38,30)(33,47,43,35)(41,46)(44,48);(18,19,26,28,40,45,21,36,24,29,22,38,23,30,37,25)(20,32,39,48,47,27,43,44,34,49,31,41,35,42,33,46);(18,20,21,33,23,35,26,31,24,34,37,43,40,47,22,39)(19,27,25,41,30,32,38,44,29,42,36,48,45,49,28,46)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6144);