Finite Group DatabasebetaFinite Group Databasebeta| order | 9212 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×Dic49 |
| unambiguous semidirect product | C49⋊(C4×C47) |
| derived, Sylow | C49 ⋊ C4×C47 |
| Hall | C47×C49 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C47 | D49 |
| commutator, hypocenter | C49 | C4×C47 |
| Frattini | C2×C7 | D7×C47 |
| Fitting | C2×C47×C49 | C2 |
| socle | C2×C7×C47 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C47 | |
18 conjugacy classes of subgroups.
2444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×(C49⋊C3)⋊C4, C3×C47×Dic49, C47×Dic147 |
| maximal normal subgroup of | C47×(C49⋊C3)⋊C4, C3×C47×Dic49 |
| maximal quotient of | C3×C47×Dic49, C47×Dic147 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9212, 2);