Finite Group DatabasebetaFinite Group Databasebeta| order | 9212 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C47 · Schur multiplier (H2) = C2 |
| direct product | C2×C47×D49 |
| unambiguous semidirect product | C49⋊(C22×C47) |
| unambiguous semidirect product | (C2×C49)⋊(C2×C47) |
| Fitting | C2×C47×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C22×C47 |
| Hall | C47×C49 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C47 | D49 |
| commutator, hypocenter | C49 | C22×C47 |
| Frattini | C7 | C2×D7×C47 |
| Fitting | C2×C47×C49 | C2 |
| socle | C2×C7×C47 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C47 | |
30 conjugacy classes of subgroups.
2444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C47×D49⋊C3, D3×C47×D49, C2×C3×C47×D49, … |
| maximal normal subgroup of | C2×C47×D49⋊C3, C2×C3×C47×D49 |
| maximal quotient of | D3×C47×D49, C2×C3×C47×D49, C2×C47×D147 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9212, 8);