Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8603 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#13107 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #117 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | #432 |
| prime radical | C23×C17 | C2×M16 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C17×#97 ◁ G | |
270 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)(22,23,28,24,26,31,37,34,29,32,36,35,27,30,25,33);(22,24,28,31,26,34,37,32,29,35,36,30,27,33,25,23);(19,21)(22,25,26,28,29,37,27,36)(23,24,30,33,32,35,31,34)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6095);