Finite Group DatabasebetaFinite Group Databasebeta| order | 9212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D47×D49 |
| unambiguous semidirect product | (C47×D49)⋊C2 |
| unambiguous semidirect product | (C49×D47)⋊C2 |
| unambiguous semidirect product | D2303⋊C2 |
| Fitting, derived, Hall | C47×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C47×C49 | C22 |
| Frattini | C7 | D7×D47 |
| socle | C7×C47 | C2×D7 |
| LCS | G ▷ C47×C49 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
650 conjugacy classes — view the full character table.
| maximal subgroup of | D47×D49⋊C3, C3×D47×D49, D47×D147, … |
| maximal normal subgroup of | D47×D49⋊C3, C3×D47×D49 |
| maximal quotient of | C3×D47×D49, D47×D147, D49×D141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9212, 6);