Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×D29⋊C16 |
| derived, Sylow | C29 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #1181 |
| commutator, hypocenter | C29 | C2×C4×C16 |
| Frattini | C2×C4 | C22×#1181 |
| Fitting | C4×C8×C29 | C4 |
| socle | C22×C29 | C22×C8 |
| prime radical | C22×D29 | C2×C8 |
| cosocle | C2×#6597 | C23 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C4×C8 | |
216 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1856 |
352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20707);