Finite Group DatabasebetaFinite Group Databasebeta| order | 22188 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #26012696⋊C2 |
| Fitting, socle, derived, Sylow | C432 ⋊ C22×C3 |
| Hall | D432 ⋊ C3 |
| Hall | #19149816 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C432 | C22×C3 |
| LCS | G ▷ C432 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 258 |
Polycyclic presentation:
2^2,3,43^2|e^a=e^42,d^b=d^42,d^c=d^36,e^c=e^6187 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22188, 39);