Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C29 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle, Hall | C22×C7×C29 ⋊ C32 |
| derived, Hall | C22×C7 ⋊ C32×C29 |
| Hall | C7×C29 ⋊ C3×A4 |
| Hall | C22×C29 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×A4×C29 |
| Sylow | C22 ⋊ C3×ΓL(1,𝔽8)×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | A4×ΓL(1,𝔽8) |
| commutator, hypocenter | C22×C7 | C32×C29 |
| Frattini | C1 | G |
| Fitting, socle | C22×C7×C29 | C32 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C29 | |
56 conjugacy classes of subgroups.
580 conjugacy classes — view the full character table.
| maximal subgroup of | C5×A4×ΓL(1,𝔽8)×C29, ΓL(1,𝔽8)×C29×A5 |
| maximal normal subgroup of | C5×A4×ΓL(1,𝔽8)×C29 |
| maximal quotient of | C5×A4×ΓL(1,𝔽8)×C29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 108);