Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×#6599 |
| derived, Sylow | C29 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #1181 |
| commutator, hypocenter | C29 | C42×C8 |
| Frattini | C23 | C22×#1181 |
| Fitting | C2×C42×C29 | C4 |
| socle, prime radical | C23×C29 | C22×C4 |
| cosocle | C22×Dic29 | C23 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C42 | |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3712 |
352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20162);