Finite Group DatabasebetaFinite Group Databasebeta| order | 6228 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C173 ⋊ C4 |
| Sylow | C173 ⋊ #157 |
| Sylow | C32 ⋊ #10621924 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C173 | C4 |
| LCS | G ▷ C32×C173 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,173|a^2=b,c^a=cd,d^a=cd^2,e^a=e^93,c^b=c^2,d^b=d^2,e^b=e^172393 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#20262014, #44528164, #44528165, … |
| maximal normal subgroup of | C5×#20262014 |
| maximal quotient of | C5×#20262014, #44528164, #44528165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6228, 29);