Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#22469 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator | C22 | C23×C8×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C23×C17 | C23×C4 |
| prime radical | C22×#41×C17 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
1500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 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)(23,26)(27,29)(30,31,32,34,33,35,36,37);(22,23)(24,27)(25,26)(28,29);(19,21)(22,24,25,28)(23,27,26,29);(23,26)(27,29)1700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15457);