Finite Group DatabasebetaFinite Group Databasebeta| order | 1582 |
| isoclinism | isoclinic class of D113⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D113⋊C7 |
| unambiguous semidirect product | (C113⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C113 ⋊ C2×C7 |
| Hall | C113⋊C7 ⋊ C2 |
| Hall | D113 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C113 | C2×C7 |
| LCS | G ▷ C113 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 113 |
Polycyclic presentation:
2,7,113|c^a=c^112,c^b=c^4922 conjugacy classes — view the full character table.
| maximal subgroup of | #90673⋊C7, C2×D113⋊C7, C3×D113⋊C7, … |
| maximal normal subgroup of | #90673⋊C7, C2×D113⋊C7, C3×D113⋊C7, … |
| maximal quotient of | Dic113⋊C7, C2×D113⋊C7, C3×D113⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1582, 1);