Finite Group DatabasebetaFinite Group Databasebeta| order | 7332 |
| automorphism | Aut(G) order 4047264 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3666 |
| direct product | C2×D1833 |
| unambiguous semidirect product | (C2×C3)⋊D611 |
| unambiguous semidirect product | (C2×C13)⋊D141 |
| unambiguous semidirect product | (C2×C47)⋊D39 |
| Fitting, socle | C2×C3×C13×C47 ⋊ C2 |
| derived, Hall | C3×C13×C47 ⋊ C22 |
| Hall | C13×C47 ⋊ C2×D3 |
| Hall | C3×C47 ⋊ C2×D13 |
| Sylow | C47 ⋊ C2×D39 |
| Hall | C3×C13 ⋊ C2×D47 |
| Sylow | C13 ⋊ C2×D141 |
| Sylow | C3 ⋊ C2×D611 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1833 |
| commutator, hypocenter | C3×C13×C47 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13×C47 | C2 |
| LCS | G ▷ C3×C13×C47 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
1836 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5499, C2×C3⋊((C13⋊C3)⋊D47), D3×D1833, … |
| maximal normal subgroup of | C2×C3⋊((C13⋊C3)⋊D47), C2×C3×D1833, C2×C5×D1833, … |
| maximal quotient of | C2×D5499, D3×D1833, C2×C3×D1833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7332, 34);