Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | #95×#1181 |
| Fitting | C29×#95 ⋊ C4 |
| Sylow | C29 ⋊ C4×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#1181 |
| commutator | C2×C29 | C43 |
| Fitting | C29×#95 | C4 |
| socle | C23×C29 | C22×C4 |
| prime radical, cosocle | C23×D29 | C23 |
| hypercenter | #95 | #1181 |
| hypocenter | C29 | C4×#95 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #95 | |
752 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 19681);