Finite Group DatabasebetaFinite Group Databasebeta| order | 22188 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C43 |
| direct product | C3×C43⋊Dic43 |
| derived, Sylow | C432 ⋊ C3×C4 |
| Hall | C3×C432 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C43⋊D43 |
| commutator, hypocenter | C432 | C3×C4 |
| Frattini | C2 | C3×C43⋊D43 |
| Fitting, socle, prime radical | C2×C3×C432 | C2 |
| cosocle | C2×C432 | C2×C3 |
| LCS | G ▷ C432 | |
| UCS | C1 ◁ C2×C3 | |
276 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22188 |
5556 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22188, 29);