Finite Group DatabasebetaFinite Group Databasebeta| order | 8722 |
| isoclinism | isoclinic class of D89 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D89 |
| unambiguous semidirect product | C89⋊(C2×C72) |
| Fitting, socle, Hall | C72×C89 ⋊ C2 |
| derived, Sylow | C89 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D89 |
| commutator, hypocenter | C89 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C89 | C2 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
2254 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×#67063, C7×C7⋊#67063, C7×D7×D89, … |
| maximal normal subgroup of | C72×#67063, C7×C7⋊#67063, C7×D7×D89, … |
| maximal quotient of | C72×Dic89, C2×C72×D89, C3×C72×D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8722, 6);