Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13215 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#13215 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1961 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
466 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)(20,31)(21,36,40,45)(22,34)(23,28)(24,30)(25,29)(26,39,44,42)(27,32)(33,38,43,48)(35,41)(37,46,49,47);(18,20,32,30,23,35,41,28,24,27,31,19,25,34,22,29)(21,37,46,45,39,43,38,44,40,49,47,36,42,33,48,26);(18,21,24,40)(19,26)(20,33)(22,38,41,48)(23,39,25,42)(27,43)(28,36)(29,45)(30,44)(31,46,32,47)(34,49)(35,37)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6203);