Finite Group DatabasebetaFinite Group Databasebeta| order | 7164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C199⋊#157 |
| Fitting, socle, derived, Hall | C32×C199 ⋊ C4 |
| Sylow | C199 ⋊ #157 |
| Sylow | C32 ⋊ Dic199 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C199 | C4 |
| LCS | G ▷ C32×C199 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,199|a^2=b,c^a=cd,d^a=cd^2,e^a=e^198,c^b=c^2,d^b=d^2600 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C199⋊#157, C199⋊#4380, C199⋊#4379 |
| maximal normal subgroup of | C5×C199⋊#157 |
| maximal quotient of | C5×C199⋊#157, C199⋊#4380, C199⋊#4379 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7164, 43);