Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C7×C3⋊D87 |
| unambiguous semidirect product | (C2×C3)⋊(C7×D87) |
| Fitting, socle | C2×C32×C7×C29 ⋊ C2 |
| derived, Hall | C32×C29 ⋊ C22×C7 |
| Hall | C32×C7×C29 ⋊ C22 |
| Hall | C7×C29 ⋊ C2×C3⋊D3 |
| Hall | C32×C7 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C7×C3⋊D3 |
| Sylow | C32 ⋊ C2×C7×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C3⋊D87 |
| commutator, hypocenter | C32×C29 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C7×C29 | C2 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 ◁ C2×C7 | |
120 conjugacy classes of subgroups.
1848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D5×C3⋊D87, C2×C5×C7×C3⋊D87, C2×C7×C3⋊D435 |
| maximal normal subgroup of | C2×C5×C7×C3⋊D87 |
| maximal quotient of | C7×D5×C3⋊D87, C2×C5×C7×C3⋊D87, C2×C7×C3⋊D435 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 157);