Finite Group DatabasebetaFinite Group Databasebeta| order | 7372 |
| automorphism | Aut(G) order 6369408 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3686 |
| direct product | C2×D1843 |
| unambiguous semidirect product | (C2×C19)⋊D97 |
| unambiguous semidirect product | (C2×C97)⋊D19 |
| Fitting, socle | C2×C19×C97 ⋊ C2 |
| derived, Hall | C19×C97 ⋊ C22 |
| Sylow | C97 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1843 |
| commutator, hypocenter | C19×C97 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C97 | C2 |
| LCS | G ▷ C19×C97 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1846 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#26010892, C2×#26010893, C2×(C19⋊C3)⋊D97, … |
| maximal normal subgroup of | C2×#26010892, C2×#26010893, C2×(C19⋊C3)⋊D97, … |
| maximal quotient of | D3×D1843, C2×C3×D1843, C2×D5529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7372, 9);