Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#13108 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #387 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1917 |
| prime radical | C23×C17 | #131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C8×C17 ◁ G | |
246 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)(18,19,23,30,24,28,42,47,25,29,43,31,22,38,40,34)(20,21,27,37,32,26,44,45,33,36,46,41,39,35,49,48);(18,20,23,27,24,32,42,44,25,33,43,46,22,39,40,49)(19,26,30,45,28,36,47,41,29,35,31,48,38,21,34,37);(18,21,22,35,25,36,24,26)(19,27,28,44,29,46,38,49)(20,31,32,34,33,30,39,47)(23,41,40,45,43,37,42,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6096);