Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D11×C22⋊D11 |
| Fitting | C22×C112 ⋊ C22 |
| Sylow | C112 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D112 |
| commutator, socle, cosocle | C2×C112 | C23 |
| Fitting | C22×C112 | C22 |
| hypercenter | C22 | D112 |
| hypocenter | C112 | C2×D4 |
| LCS | G ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C2 ◁ C22 | |
148 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 88 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | #72222476, D4×D112, #72222620, … |
| maximal normal subgroup of | #72222476, D4×D112, #72222620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 133);