Finite Group DatabasebetaFinite Group Databasebeta| order | 6228 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C173 · Schur multiplier (H2) = C3 |
| direct product | #157×C173 |
| Fitting, socle, Hall | C32×C173 ⋊ C4 |
| derived, Sylow | C32 ⋊ C4×C173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C173 | #157 |
| commutator, hypocenter | C32 | C4×C173 |
| Frattini | C1 | G |
| Fitting, socle | C32×C173 | C4 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C173 | |
20 conjugacy classes of subgroups.
1038 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#157×C173, C173×#4380, C173×#4379 |
| maximal normal subgroup of | C5×#157×C173 |
| maximal quotient of | C5×#157×C173, C173×#4380, C173×#4379 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6228, 28);