Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| isoclinism | isoclinic class of #64423 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3 |
| direct product | C3×C13×#64423 |
| Fitting, socle | C3×C72×C13 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C32×C13 |
| Hall | C3×C13×#3861 ⋊ C2 |
| Hall | C7×C13×D7 ⋊ C32 |
| Hall | C72×C13 ⋊ C2×C32 |
| Hall | C3×#3861 ⋊ C2×C13 |
| Hall | C7×D7 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | #64423 |
| commutator, cosocle, hypocenter | C72 | C2×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C13 | |
132 conjugacy classes of subgroups.
663 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D13×#64423, C3×C13×#64423⋊C2, C3×#64423⋊D13, … |
| maximal normal subgroup of | C3×D13×#64423, C3×C13×#64423⋊C2, C3×#64423⋊D13, … |
| maximal quotient of | C3×C13×#10596873, C2×C3×C13×#64423 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 242);