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×#13158 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1936 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
316 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)(18,19,24,29,26,30,25,40)(20,22,28,41,33,31,43,23)(21,34,38,49,39,35,44,32)(27,45,46,37,48,36,47,42);(18,20,31,29,25,28,41,30,26,33,22,40,24,43,23,19)(21,35,36,27,38,49,42,47,39,34,45,48,44,32,37,46);(18,21,22,36,25,38,23,42,26,39,31,45,24,44,41,37)(19,27,20,32,29,47,28,35,30,48,33,49,40,46,43,34)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6146);