Finite Group DatabasebetaFinite Group Databasebeta| order | 7164 |
| automorphism | Aut(G) order 4255416 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3582 |
| direct product | C2×D1791 |
| unambiguous semidirect product | (C2×C9)⋊D199 |
| unambiguous semidirect product | (C2×C199)⋊D9 |
| Fitting | C2×C9×C199 ⋊ C2 |
| derived, Hall | C9×C199 ⋊ C22 |
| Sylow | C199 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D199 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1791 |
| commutator, hypocenter | C9×C199 | C22 |
| Frattini | C3 | C2×D597 |
| Fitting | C2×C9×C199 | C2 |
| socle | C2×C3×C199 | D3 |
| LCS | G ▷ C9×C199 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
1794 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1791, C2×D8955, C2×C5×D1791, … |
| maximal normal subgroup of | C2×C5×D1791, D7164 |
| maximal quotient of | D5×D1791, C2×D8955, C2×C5×D1791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7164, 15);