Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×C7×Dic29 |
| derived, Sylow | C29 ⋊ C32×C4×C7 |
| Hall | C32×C7×C29 ⋊ C4 |
| Hall | C32×C29 ⋊ C4×C7 |
| Hall | C7×C29 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C7 | D29 |
| commutator, hypocenter | C29 | C32×C4×C7 |
| Frattini | C2 | C32×C7×D29 |
| Fitting, socle | C2×C32×C7×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C32×C7 | |
72 conjugacy classes of subgroups.
2016 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C7×Dic145, C32×C5×C7×Dic29, C32×C7×#10596816 |
| maximal normal subgroup of | C32×C5×C7×Dic29 |
| maximal quotient of | C32×C7×Dic145, C32×C5×C7×Dic29, C32×C7×#10596816 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 68);