Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | D29×M64 |
| Fitting | C29×M64 ⋊ C2 |
| Sylow | C29 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D29 |
| commutator, socle | C2×C29 | C22×C16 |
| Fitting | C29×M64 | C2 |
| prime radical | C22×D29 | C16 |
| cosocle | C16×C29 | C23 |
| hypercenter | M64 | D29 |
| hypocenter | C29 | C2×M64 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C16 ◁ M64 | |
112 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 6800);