Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D29×D32 |
| Fitting | C29×D32 ⋊ C2 |
| Sylow | C29 ⋊ C2×D32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D29 |
| commutator, cosocle | C16×C29 | C23 |
| Frattini | C16 | C22×D29 |
| Fitting | C29×D32 | C2 |
| socle | C2×C29 | C2×D16 |
| hypercenter | D32 | D29 |
| hypocenter | C29 | C2×D32 |
| LCS | G ▷ C16×C29 ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 6806);