Finite Group DatabasebetaFinite Group Databasebeta| order | 7372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D19×D97 |
| unambiguous semidirect product | (D19×C97)⋊C2 |
| unambiguous semidirect product | (C19×D97)⋊C2 |
| unambiguous semidirect product | D1843⋊C2 |
| Fitting, socle, derived, Hall | C19×C97 ⋊ C22 |
| Sylow | C97 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C97 | C22 |
| LCS | G ▷ C19×C97 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
550 conjugacy classes — view the full character table.
| maximal subgroup of | #26010884⋊C2, #26010885⋊C2, D19⋊C3×D97, … |
| maximal normal subgroup of | #26010884⋊C2, #26010885⋊C2, D19⋊C3×D97, … |
| maximal quotient of | C3×D19×D97, D57×D97, D19×D291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7372, 8);