Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #11760329⋊C7 |
| Fitting, socle, derived, Hall | C32×C29 ⋊ C4×C7 |
| Hall | C32×C29⋊C7 ⋊ C4 |
| Hall | #11760329 ⋊ C7 |
| Hall | C29⋊C7 ⋊ #157 |
| Sylow | C29 ⋊ C7×#157 |
| Sylow | C32 ⋊ AGL(1,𝔽29) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C29 | C4×C7 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,2,3^2,29|a^2=c,d^a=de,e^a=de^2,f^a=f^17,f^b=f^16,d^c=d^2,e^c=e^2,f^c=f^2851 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#11760329⋊C7, #19104885⋊C7, #19104886⋊C7, … |
| maximal normal subgroup of | C5×#11760329⋊C7 |
| maximal quotient of | C5×#11760329⋊C7, #19104885⋊C7, #19104886⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 88);