Finite Group DatabasebetaFinite Group Databasebeta| order | 9212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D329 |
| unambiguous semidirect product | (C7×D7)⋊D47 |
| unambiguous semidirect product | (D7×C47)⋊D7 |
| Fitting, socle, derived, Hall | C72×C47 ⋊ C22 |
| Sylow | C72 ⋊ C2×D47 |
| Sylow | C47 ⋊ D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C47 | C22 |
| LCS | G ▷ C72×C47 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
830 conjugacy classes — view the full character table.
| maximal subgroup of | #64418⋊D47, D7×ΓL(1,𝔽8)⋊D47, AGL(1,𝔽7)×D329, … |
| maximal normal subgroup of | D7×ΓL(1,𝔽8)⋊D47, AGL(1,𝔽7)×D329, #64423⋊D47, … |
| maximal quotient of | C3×D7×D329, D7×D987, D21×D329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9212, 20);