Finite Group DatabasebetaFinite Group Databasebeta| order | 11936 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#20238613 |
| derived, Sylow | C373 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #13093637 |
| commutator, hypocenter | C373 | C2×C16 |
| Frattini | C4 | C2×#13093637 |
| Fitting | C2×C4×C373 | C4 |
| socle, prime radical | C22×C373 | C8 |
| cosocle | #15688412 | C22 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
776 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#20238613, #37560308, #37560310, … |
| maximal normal subgroup of | C4×#20238613, #37560308, #37560310, … |
| maximal quotient of | C4×#20238613, C22⋊#20238613, C4⋊#20238613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11936, 218);