Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#4294⋊C4 |
| unambiguous semidirect product | #4294⋊(C4×C13) |
| derived, Sylow | C19 ⋊ C4×C9×C13 |
| Hall | C13×#4294 ⋊ C4 |
| Hall | C13×Dic19 ⋊ C9 |
| Hall | C13×C19 ⋊ C4×C9 |
| Hall | #4294 ⋊ C4×C13 |
| Hall | Dic19 ⋊ C9×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C13 | D19⋊C3 |
| commutator, hypocenter | C19 | C4×C9×C13 |
| Frattini | C2×C3 | C13×D19⋊C3 |
| Fitting, socle | C2×C3×C13×C19 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C3×C13 | |
36 conjugacy classes of subgroups.
702 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 2);