Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9263 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C17×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
478 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)(19,24,26,33)(20,28,30,47)(21,32)(27,39,38,48)(29,46,34,31)(36,45)(37,44)(40,41);(18,19,21,33,35,38,45,39)(20,25,34,40,46,49,28,44)(22,27,32,48,23,26,36,24)(29,37,31,42,47,41,30,43);(18,20)(19,25)(21,34)(22,31)(23,30)(24,37)(26,43)(27,42)(28,45)(29,36)(32,47)(33,40)(35,46)(38,49)(39,44)(41,48)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2251);