Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#8029 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C22⋊C4 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C23×C17 | C2×C22⋊C4 |
| prime radical | C24×C17 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C22×C42×C17 ◁ G | |
746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2176 |
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)(24,26)(25,28)(27,29)(30,31,34,37)(32,35,36,33);(23,26,28,27)(30,32,35,31,34,36,33,37);(30,33,34,35)(31,32,37,36)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1017);