Finite Group DatabasebetaFinite Group Databasebeta| order | 6228 |
| automorphism | Aut(G) order 3213648 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3114 |
| direct product | C2×D1557 |
| unambiguous semidirect product | (C2×C9)⋊D173 |
| unambiguous semidirect product | (C2×C173)⋊D9 |
| Fitting | C2×C9×C173 ⋊ C2 |
| derived, Hall | C9×C173 ⋊ C22 |
| Sylow | C173 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1557 |
| commutator, hypocenter | C9×C173 | C22 |
| Frattini | C3 | C2×D519 |
| Fitting | C2×C9×C173 | C2 |
| socle | C2×C3×C173 | D3 |
| LCS | G ▷ C9×C173 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
1560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1557, C2×D7785, C2×C5×D1557, … |
| maximal normal subgroup of | C2×C5×D1557, D6228 |
| maximal quotient of | D5×D1557, C2×D7785, C2×C5×D1557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6228, 10);