Finite Group DatabasebetaFinite Group Databasebeta| order | 11936 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#15688412 |
| derived, Sylow | C373 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D373 |
| commutator, hypocenter | C373 | C22×C8 |
| Frattini | C4 | C22×D373 |
| Fitting | C22×C4×C373 | C2 |
| socle, prime radical | C23×C373 | C4 |
| cosocle | C4×C373 | C23 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
3008 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37559176, #37559177, #37559184, … |
| maximal normal subgroup of | #37559176, #37559177, #37559184, … |
| maximal quotient of | C2×C4×#15688412, C2×C22⋊#15688412, C2×C4⋊#15688412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11936, 148);