Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C17 · Schur multiplier (H2) = C22×C42 |
| direct product | C17×#10705 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C2×D4 |
| commutator | C4 | C43×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C23×C17 | C2×C4⋊C4 |
| prime radical | C24×C17 | C2×Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C22×C42×C17 ◁ G | |
870 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(26,27,29,34,31,35,30,33)(28,36,38,32,37,41,39,40);(19,21)(26,28,30,39,31,37,29,38)(27,32,34,41,35,40,33,36);(22,23,24,25)(28,37)(32,40)(36,41)(38,39)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3693);