Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×Dic3×C29 |
| unambiguous semidirect product | C3⋊(C3×C4×C7×C29) |
| derived | C3 ⋊ C3×C4×C7×C29 |
| Hall | C32×C7×C29 ⋊ C4 |
| Hall | C32×C29 ⋊ C4×C7 |
| Hall | C32×C7 ⋊ C4×C29 |
| Sylow | C32 ⋊ C4×C7×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7×C29 | D3 |
| commutator, hypocenter | C3 | C3×C4×C7×C29 |
| Frattini | C2 | C3×D3×C7×C29 |
| Fitting, socle | C2×C32×C7×C29 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C3×C7×C29 | |
56 conjugacy classes of subgroups.
3654 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×C29×Dic15, C3×C5×C7×Dic3×C29, C3×C7×C29×ΓL(1,𝔽16) |
| maximal normal subgroup of | C3×C5×C7×Dic3×C29 |
| maximal quotient of | C3×C7×C29×Dic15, C3×C5×C7×Dic3×C29, C3×C7×C29×ΓL(1,𝔽16) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 71);