Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #10625202⋊A4 |
| Fitting, socle, derived, Hall | C22×C13×C19 ⋊ C32 |
| Hall | C13×C19 ⋊ C3×A4 |
| Hall | C22×C19 ⋊ C3×C13⋊C3 |
| Hall | C22×C13 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ A4×C13⋊C3 |
| Sylow | C13 ⋊ A4×C19⋊C3 |
| Sylow | C22 ⋊ C13⋊C3×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C13×C19 | C32 |
| LCS | G ▷ C22×C13×C19 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,2^2,13,19|e^a=e^3,f^a=f^7,c^b=cd,d^b=c,e^b=e^3148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 219);