Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11522 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12720 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #410 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| socle | C2×C17 | #1782 |
| prime radical | C17×#3455 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C42×C17 ◁ C4×#41×C17 ◁ G | |
694 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)(20,29)(21,34,36,26)(22,27)(23,28)(24,31,40,30)(25,35,42,49)(32,41)(33,45)(37,43)(38,48)(39,47,44,46);(18,20)(19,24)(21,31)(22,32)(23,33)(25,41)(26,29)(27,39)(28,40)(30,36)(34,45)(35,47)(37,48)(38,42)(43,44)(46,49);(18,21)(19,25,28,42)(20,30)(22,35)(23,36)(24,38,40,41)(26,27,34,43)(29,44,45,39)(31,33)(32,46)(37,49)(47,48)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5708);