Finite Group DatabasebetaFinite Group Databasebeta| order | 11638 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C232 ⋊ C2×C11 |
| Hall | #19154123 ⋊ C2 |
| Hall | C23×D23 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C232 | C2×C11 |
| LCS | G ▷ C232 | |
| UCS | C1 | |
17 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,23^2|c^a=c^22,c^b=c^2,d^b=d^649 conjugacy classes — view the full character table.
| maximal subgroup of | #26042791⋊C2, C2×#26042801, C3×#26042801, … |
| maximal normal subgroup of | #26042791⋊C2, C2×#26042801, C3×#26042801 |
| maximal quotient of | #37551740, C2×#26042801, C3×#26042801, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11638, 23);