Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×#14271071 |
| Fitting | C23×D4×C29 ⋊ C2 |
| Sylow | C29 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D29 |
| commutator, cosocle | C23×C29 | C24 |
| Frattini | C23 | C23×D29 |
| Fitting | C23×D4×C29 | C2 |
| socle | C24×C29 | C23 |
| hypercenter | C23×D4 | D29 |
| hypocenter | C29 | C2×#392 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
1812 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1856 |
604 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 7705);