Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11499 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12689 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#99 |
| commutator | C24 | C22×C4×C17 |
| Frattini, cosocle | C22×D4 | C23×C17 |
| prime radical | C2×C17×#525 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C22×#41×C17 ◁ G | |
1160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,28)(25,32,33,27)(26,29)(30,36,37,34)(31,35);(23,27)(28,34)(29,32)(35,36);(19,21)(22,24,26,31)(23,28,29,35)(25,30,33,37)(27,34,32,36)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5677);