Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#20608 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| socle | C22×C17 | C2×#120 |
| prime radical | C2×C17×#585 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
3798 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1088 |
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)(22,23)(24,30,32,27)(25,28)(26,29)(31,36,37,34)(33,35);(22,24)(23,27)(25,31)(26,32)(28,34)(29,30)(33,37)(35,36);(19,21)(22,23)(24,27)(25,28)(26,29)(30,32)(31,34)(33,35)(36,37);(22,25,26,33)(23,28,29,35)(24,31,32,37)(27,34,30,36)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13596);