Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C4×#1181 |
| unambiguous semidirect product | D29⋊(C22×C42) |
| Fitting | C23×C4×C29 ⋊ C4 |
| derived, Sylow | C29 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #1181 |
| commutator, hypocenter | C29 | C23×C42 |
| Frattini | C2 | C24×#1181 |
| Fitting | C23×C4×C29 | C4 |
| socle | C24×C29 | C2×C4 |
| prime radical | C24×D29 | C22 |
| cosocle | C2×D29 | C25 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C23×C4 | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 21480);