Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13163 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C2×D4 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×C4⋊C8 |
| prime radical | C23×C17 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
318 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)(19,21)(22,23,26,24,25,29,34,32,27,30,36,33,35,28,37,31);(22,24,26,29,25,32,34,30,27,33,36,28,35,31,37,23);(18,19,20,21)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6151);