Finite Group DatabasebetaFinite Group Databasebeta| order | 11936 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D373⋊C8 |
| unambiguous semidirect product | D373⋊(C2×C8) |
| derived, Sylow | C373 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #13093637 |
| commutator, hypocenter | C373 | C22×C8 |
| Frattini | C2 | C22×#13093637 |
| Fitting | C2×C4×C373 | C4 |
| socle | C22×C373 | C2×C4 |
| prime radical | C22×D373 | C4 |
| cosocle | Dic373 | C23 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
776 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#13093637)⋊C8, #37560295, #37560297, … |
| maximal normal subgroup of | (C2×#13093637)⋊C8, #37560295, #37560297, … |
| maximal quotient of | C2×C4×#15688419, C4×D373⋊C8, D373⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11936, 229);