Finite Group DatabasebetaFinite Group Databasebeta| order | 11936 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×Dic373 |
| derived, Sylow | C373 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D373 |
| commutator, hypocenter | C373 | C4×C8 |
| Frattini | C2×C4 | C2×D373 |
| Fitting | C2×C8×C373 | C2 |
| socle, prime radical | C22×C373 | C2×C4 |
| cosocle | C2×C4×C373 | C22 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C2×C8 | |
44 conjugacy classes of subgroups.
3008 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic373, #37559197, #37559240, … |
| maximal normal subgroup of | C16×Dic373, #37559197, #37559240, … |
| maximal quotient of | C8×#15688412, #37559144, #37559176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11936, 54);