Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C29 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic7×C29 |
| derived, Sylow | C7 ⋊ C4×C9×C29 |
| Hall | C7×C9×C29 ⋊ C4 |
| Hall | C7×C29 ⋊ C4×C9 |
| Hall | C7×C9 ⋊ C4×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9×C29 | D7 |
| commutator, hypocenter | C7 | C4×C9×C29 |
| Frattini | C2×C3 | C3×D7×C29 |
| Fitting | C2×C7×C9×C29 | C2 |
| socle | C2×C3×C7×C29 | C2×C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C9×C29 | |
36 conjugacy classes of subgroups.
2610 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C9×Dic7×C29, C9×C29×Dic35, C9×C29×C7⋊AGL(1,𝔽5) |
| maximal normal subgroup of | C5×C9×Dic7×C29 |
| maximal quotient of | C5×C9×Dic7×C29, C9×C29×Dic35, C9×C29×C7⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 11);