Finite Group DatabasebetaFinite Group Databasebeta| order | 17524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#13062438 |
| Fitting, socle, Hall | C13×C337 ⋊ C4 |
| derived, Sylow | C337 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #13062438 |
| commutator, hypocenter | C337 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C337 | C4 |
| prime radical | C13×D337 | C2 |
| cosocle | D337 | C2×C13 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C13 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4381 |
1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17524, 6);