Finite Group DatabasebetaFinite Group Databasebeta| order | 9212 |
| automorphism | Aut(G) order 8898792 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4606 |
| direct product | C2×D2303 |
| unambiguous semidirect product | (C2×C47)⋊D49 |
| unambiguous semidirect product | (C2×C49)⋊D47 |
| Fitting | C2×C47×C49 ⋊ C2 |
| derived, Hall | C47×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2303 |
| commutator, hypocenter | C47×C49 | C22 |
| Frattini | C7 | C2×D329 |
| Fitting | C2×C47×C49 | C2 |
| socle | C2×C7×C47 | D7 |
| LCS | G ▷ C47×C49 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
2306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C47⋊(D49⋊C3), D3×D2303, C2×C3×D2303, … |
| maximal normal subgroup of | C2×C47⋊(D49⋊C3), C2×C3×D2303, D9212 |
| maximal quotient of | D3×D2303, C2×C3×D2303, C2×D6909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9212, 9);