Finite Group DatabasebetaFinite Group Databasebeta| order | 11774 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×#19154635 |
| Fitting, socle, Hall | C2×C292 ⋊ C7 |
| derived, Sylow | C292 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19154635 |
| commutator, cosocle, hypocenter | C292 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C292 | C7 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
254 conjugacy classes — view the full character table.
| maximal subgroup of | #37555387, #37555388, #37555391, … |
| maximal normal subgroup of | #37555387, #37555388, #37555391, … |
| maximal quotient of | C4×#19154635, C22×#19154635, D3×#19154635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11774, 24);