Finite Group DatabasebetaFinite Group Databasebeta| order | 22188 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C432 ⋊ C3×C4 |
| Hall | C43×Dic43 ⋊ C3 |
| Hall | #19149815 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #26012695 |
| commutator, hypocenter | C432 | C3×C4 |
| Fitting, socle, cosocle | C2×C432 | C2×C3 |
| prime radical | C2×#19149815 | C2 |
| LCS | G ▷ C432 | |
| UCS | C1 ◁ C2 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 172 |
Polycyclic presentation:
2,3,43^2,2|a^2=e,d^a=d^42,c^b=c^36,d^b=d^36670 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22188, 21);