Finite Group DatabasebetaFinite Group Databasebeta| order | 9492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D21⋊D113 |
| unambiguous semidirect product | D339⋊D7 |
| unambiguous semidirect product | D791⋊D3 |
| Fitting, socle, derived, Hall | C3×C7×C113 ⋊ C22 |
| Hall | C7×C113 ⋊ C2×D3 |
| Hall | C3×C113 ⋊ C2×D7 |
| Sylow | C113 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×D113 |
| Sylow | C7 ⋊ D3×D113 |
| Sylow | C3 ⋊ D7×D113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C113 | C22 |
| LCS | G ▷ C3×C7×C113 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7,113|d^a=d^6,e^a=e^112,c^b=c^2,d^b=d^6687 conjugacy classes — view the full character table.
| maximal subgroup of | D63⋊D113, (C3⋊AGL(1,𝔽7))⋊D113, C3×D21⋊D113, … |
| maximal normal subgroup of | (C3⋊AGL(1,𝔽7))⋊D113, C3×D21⋊D113 |
| maximal quotient of | D63⋊D113, C3×D21⋊D113, D339⋊D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9492, 42);