Finite Group DatabasebetaFinite Group Databasebeta| order | 882 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C7 |
| direct product | C9×C7⋊D7 |
| Fitting, Hall | C72×C9 ⋊ C2 |
| derived, Sylow | C72 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C7⋊D7 |
| commutator, hypocenter | C72 | C2×C9 |
| Frattini | C3 | C3×C7⋊D7 |
| Fitting | C72×C9 | C2 |
| socle, cosocle | C3×C72 | C2×C3 |
| prime radical | C3×C7⋊D7 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C9 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 441 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#5997, C9⋊#5997, C9×D72, … |
| maximal normal subgroup of | C9×#5997, C9⋊#5997, C9×D72, … |
| maximal quotient of | C9×C7⋊Dic7, C2×C9×C7⋊D7, C5×C9×C7⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(882, 29);