Finite Group DatabasebetaFinite Group Databasebeta| order | 11774 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C292 ⋊ D7 |
| derived, Hall | #19154637 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #19154637 | C2 |
| Fitting, socle | C292 | D7 |
| LCS | G ▷ #19154637 | |
| UCS | C1 | |
15 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,29^2|b^a=b^6,c^a=d,d^a=c,c^b=c^25,d^b=d^7107 conjugacy classes — view the full character table.
| maximal subgroup of | #26044451⋊C2, C2×#26044451, C3×#26044451, … |
| maximal normal subgroup of | #26044451⋊C2, C2×#26044451, C3×#26044451 |
| maximal quotient of | #37555381, C2×#26044451, C3×#26044451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11774, 8);