Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C13 ⋊ C2×C32 |
| Hall | #3861⋊(C13⋊C3) ⋊ C2 |
| Hall | C72×D13 ⋊ C32 |
| Sylow | C72 ⋊ C3×D13⋊C3 |
| Hall | D13 ⋊ ΓL(1,𝔽8)2 |
| Sylow | C13 ⋊ C2×ΓL(1,𝔽8)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C13 | C2×C32 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
112 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2,3^2,7^2,13|f^a=f^12,d^b=d^2,f^b=f^3,d^c=d^2,e^c=e^288 conjugacy classes — view the full character table.
| maximal subgroup of | #37524883, #37524891, #37524892, … |
| maximal normal subgroup of | #37524883, #37524891, #37524892, … |
| maximal quotient of | #37524672, C2×#26039554 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 197);