Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×#11745144 |
| derived, Sylow | C29 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #1181 |
| commutator, hypocenter | C29 | C22×C32 |
| Frattini | C8 | C22×#1181 |
| Fitting | C22×C8×C29 | C4 |
| socle, prime radical | C23×C29 | C16 |
| cosocle | #90768 | C23 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C22×C8 | |
120 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, 20928);