Finite Group DatabasebetaFinite Group Databasebeta| order | 882 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C32×C7⋊D7 |
| Fitting, socle, Hall | C32×C72 ⋊ C2 |
| derived, Sylow | C72 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C7⋊D7 |
| commutator, cosocle, hypocenter | C72 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 441 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#5997, C3×C3⋊#5997, C3⋊(C3⋊#5997), … |
| maximal normal subgroup of | C32×#5997, C3×C3⋊#5997, C3⋊(C3⋊#5997), … |
| maximal quotient of | C32×C7⋊Dic7, C2×C32×C7⋊D7, C32×C5×C7⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(882, 61);