Finite Group DatabasebetaFinite Group Databasebeta| order | 11774 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C292 ⋊ C2×C7 |
| Hall | #19154637 ⋊ C2 |
| Hall | C29×D29 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C292 | C2×C7 |
| LCS | G ▷ C292 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,29^2|d^a=d^28,c^b=c^16,d^b=d^2080 conjugacy classes — view the full character table.
| maximal subgroup of | #37555434, #37555435, #26044463⋊C2, … |
| maximal normal subgroup of | #37555434, #37555435, #26044463⋊C2, … |
| maximal quotient of | #37555393, C2×#26044463, C3×#26044463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11774, 20);