Finite Group DatabasebetaFinite Group Databasebeta| order | 6228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D519 |
| unambiguous semidirect product | (C2×C3)⋊D519 |
| unambiguous semidirect product | (C2×C173)⋊(C3⋊D3) |
| Fitting, socle | C2×C32×C173 ⋊ C2 |
| derived, Hall | C32×C173 ⋊ C22 |
| Sylow | C173 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×D173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D519 |
| commutator, hypocenter | C32×C173 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C173 | C2 |
| LCS | G ▷ C32×C173 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
1560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×C3⋊D519, C2×C5×C3⋊D519, C2×C3⋊D2595 |
| maximal normal subgroup of | C2×C5×C3⋊D519 |
| maximal quotient of | D5×C3⋊D519, C2×C5×C3⋊D519, C2×C3⋊D2595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6228, 32);