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 | #19154634 ⋊ 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 | |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,29^2|c^a=c^28,d^a=d^28,c^b=c^16,d^b=d^1674 conjugacy classes — view the full character table.
| maximal subgroup of | #37555415, #37555416, #26044455⋊C2, … |
| maximal normal subgroup of | #37555415, #37555416, #26044455⋊C2, … |
| maximal quotient of | #37555385, C2×#26044455, C3×#26044455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11774, 12);