Finite Group DatabasebetaFinite Group Databasebeta| order | 8228 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×#595 |
| Fitting, socle, Hall | C112×C17 ⋊ C4 |
| derived, Sylow | C17 ⋊ C4×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | #595 |
| commutator, hypocenter | C17 | C4×C112 |
| Frattini | C1 | G |
| Fitting, socle | C112×C17 | C4 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C112 | |
84 conjugacy classes of subgroups.
968 conjugacy classes — view the full character table.
| maximal subgroup of | #595×C112⋊C3, C3×C112×#595, C112×C3⋊#595 |
| maximal normal subgroup of | #595×C112⋊C3, C3×C112×#595 |
| maximal quotient of | C3×C112×#595, C112×C3⋊#595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8228, 19);