Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×C7×#1181 |
| Fitting, socle, Hall | C32×C7×C29 ⋊ C4 |
| derived, Sylow | C29 ⋊ C32×C4×C7 |
| Hall | C32×C29 ⋊ C4×C7 |
| Hall | C7×C29 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | #1181 |
| commutator, hypocenter | C29 | C32×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C29 | C4 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C32×C7 | |
72 conjugacy classes of subgroups.
693 conjugacy classes — view the full character table.
| maximal subgroup of | C32×C5×C7×#1181, C32×C7×#10596814, C32×C7×#10596815, … |
| maximal normal subgroup of | C32×C5×C7×#1181 |
| maximal quotient of | C32×C5×C7×#1181, C32×C7×#10596814, C32×C7×#10596815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 117);