Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C29 · Schur multiplier (H2) = C2 |
| direct product | C22×C29×C7⋊C9 |
| derived, Sylow | C7 ⋊ C22×C9×C29 |
| Hall | C22×C7×C29 ⋊ C9 |
| Hall | C7×C29 ⋊ C22×C9 |
| Hall | C22×C7 ⋊ C9×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C29 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C22×C9×C29 |
| Frattini | C3 | C22×ΓL(1,𝔽8)×C29 |
| Fitting, socle | C22×C3×C7×C29 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C22×C3×C29 | |
60 conjugacy classes of subgroups.
1740 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5×C29×C7⋊C9, C22×C5×C29×C7⋊C9 |
| maximal normal subgroup of | C22×C5×C29×C7⋊C9 |
| maximal quotient of | C2×D5×C29×C7⋊C9, C22×C5×C29×C7⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 43);