Finite Group DatabasebetaFinite Group Databasebeta| order | 6228 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C173 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle | C22×C3×C173 ⋊ C3 |
| derived, Sylow | C22 ⋊ C32×C173 |
| Hall | C22×C173 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C173 | A4 |
| commutator, hypocenter | C22 | C32×C173 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C173 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C173 | |
28 conjugacy classes of subgroups.
2076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×A4×C173, C3×A5×C173 |
| maximal normal subgroup of | C3×C5×A4×C173 |
| maximal quotient of | C3×C5×A4×C173 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6228, 31);