Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×#1181 |
| unambiguous semidirect product | D29⋊C43 |
| Fitting | C2×C42×C29 ⋊ C4 |
| derived, Sylow | C29 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #1181 |
| commutator, hypocenter | C29 | C2×C43 |
| Frattini | C22 | C23×#1181 |
| Fitting | C2×C42×C29 | C4 |
| socle | C23×C29 | C22×C4 |
| prime radical | C23×D29 | C23 |
| cosocle | C22×D29 | C24 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C42 | |
1272 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, 20935);