Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×#11745236 |
| Fitting | C22×C42×C29 ⋊ C2 |
| Sylow | C29 ⋊ C22×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D29 |
| commutator, cosocle | C22×C29 | C25 |
| Frattini | C22 | C24×D29 |
| Fitting | C22×C42×C29 | C2 |
| socle | C24×C29 | C23 |
| hypercenter | C22×C42 | D29 |
| hypocenter | C29 | C22×#127 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 17782);