Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived | C3×C7×C29 ⋊ C22×C3 |
| Hall | C3×ΓL(1,𝔽8)×C29 ⋊ C22 |
| Hall | C7×C29 ⋊ C2×C3×D3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×D29 |
| Sylow | C29 ⋊ D3×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C2×C3×D87 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C29 | C22×C3 |
| LCS | G ▷ C3×C7×C29 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
315 conjugacy classes — view the full character table.
| maximal subgroup of | C5×AGL(1,𝔽7)×D87, AGL(1,𝔽7)×D435, D87×C5⋊AGL(1,𝔽7), … |
| maximal normal subgroup of | C5×AGL(1,𝔽7)×D87 |
| maximal quotient of | C5×AGL(1,𝔽7)×D87, AGL(1,𝔽7)×D435, D87×C5⋊AGL(1,𝔽7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 103);