Finite Group DatabasebetaFinite Group Databasebeta| order | 6132 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C73 ⋊ C3×C4 |
| Hall | C7×#64408 ⋊ C3 |
| Hall | #13095276 ⋊ C4 |
| Hall | #64408 ⋊ ΓL(1,𝔽8) |
| Sylow | C73 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ #64408⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C73 | C3×C4 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,7,73|a^2=c,e^a=e^27,d^b=d^2,e^b=e^64,e^c=e^7262 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#64408⋊C3, C3×#20259503, C3⋊#20259503, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#64408⋊C3, C3×#20259503, C5×#20259503 |
| maximal quotient of | #32913716, C3×#20259503, C3⋊#20259503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6132, 34);