Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12616 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C42 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×#97 |
| prime radical | C24×C17 | M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1088 |
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)(22,23,26,32,27,29,35,36,28,24,30,33,25,31,34,37);(19,21)(23,29,24,31)(26,30)(32,37,33,36)(34,35);(22,24,26,33,27,31,35,37,28,23,30,32,25,29,34,36)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5604);