Finite Group DatabasebetaFinite Group Databasebeta| order | 9212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D7×D47 |
| unambiguous semidirect product | (D7×C47)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D47)⋊(C2×C7) |
| unambiguous semidirect product | D329⋊(C2×C7) |
| Fitting, socle, Hall | C72×C47 ⋊ C22 |
| derived | C7×C47 ⋊ C22×C7 |
| Sylow | C72 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D7×D47 |
| commutator, hypocenter | C7×C47 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C47 | C22 |
| LCS | G ▷ C7×C47 | |
| UCS | C1 ◁ C7 | |
52 conjugacy classes of subgroups.
875 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#64418, C7×AGL(1,𝔽7)×D47, D7×ΓL(1,𝔽8)×D47, … |
| maximal normal subgroup of | C7×AGL(1,𝔽7)×D47, D7×ΓL(1,𝔽8)×D47, D47×#64423, … |
| maximal quotient of | C3×C7×D7×D47, C7×D21×D47, C7×D7×D141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9212, 17);