Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C7⋊#1181 |
| Fitting, Hall | C7×C9×C29 ⋊ C4 |
| derived, Hall | C7×C29 ⋊ C4×C9 |
| Hall | C9×C29 ⋊ Dic7 |
| Hall | C7×C9 ⋊ #1181 |
| Sylow | C29 ⋊ C9×Dic7 |
| Sylow | C7 ⋊ C9×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C7⋊#1181 |
| commutator, hypocenter | C7×C29 | C4×C9 |
| Frattini | C3 | C3×C7⋊#1181 |
| Fitting | C7×C9×C29 | C4 |
| socle | C3×C7×C29 | C3×C4 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
531 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9×C7⋊#1181, C9×C7⋊#10596814, C9×C7⋊#10596815, … |
| maximal normal subgroup of | C5×C9×C7⋊#1181 |
| maximal quotient of | C5×C9×C7⋊#1181, C9×C7⋊#10596814, C9×C7⋊#10596815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 33);