Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12753 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12754 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1790 |
| commutator | C2×D4 | C22×C4×C17 |
| Frattini, cosocle | C22×D4 | C23×C17 |
| prime radical | C17×#3533 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C23×C17 ◁ C22×D4×C17 ◁ G | |
782 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)(20,28)(21,25)(22,34,35,26)(23,27)(24,30,37,46)(29,43)(31,42)(32,40,47,38)(33,39)(36,44,48,49)(41,45);(18,20)(19,24)(21,29)(22,30)(23,31)(25,36)(26,28)(27,37)(32,44)(33,45)(34,42)(35,46)(38,43)(39,48)(40,41)(47,49);(18,21,23,33)(19,25,27,39)(20,29,31,45)(22,32,35,47)(24,36,37,48)(26,40,34,38)(28,41,42,43)(30,44,46,49)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5742);