Finite Group DatabasebetaFinite Group Databasebeta| order | 8722 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C89 · Schur multiplier (H2) = C7 |
| direct product | C89×C7⋊D7 |
| unambiguous semidirect product | C7⋊(D7×C89) |
| Fitting, socle, Hall | C72×C89 ⋊ C2 |
| derived, Sylow | C72 ⋊ C2×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | C7⋊D7 |
| commutator, hypocenter | C72 | C2×C89 |
| Frattini | C1 | G |
| Fitting, socle | C72×C89 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C89 | |
40 conjugacy classes of subgroups.
2314 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7⋊D7×D89, D72×C89, (C7⋊D7)⋊D89, … |
| maximal normal subgroup of | C7⋊D7×D89, D72×C89, (C7⋊D7)⋊D89, … |
| maximal quotient of | C89×C7⋊Dic7, C2×C89×C7⋊D7, C3×C89×C7⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8722, 9);