Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| isoclinism | isoclinic class of C3⋊D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C3 |
| direct product | C29×C3⋊Dic21 |
| unambiguous semidirect product | C3⋊(C29×Dic21) |
| unambiguous semidirect product | C7⋊(C29×C3⋊Dic3) |
| derived, Hall | C32×C7 ⋊ C4×C29 |
| Hall | C32×C7×C29 ⋊ C4 |
| Hall | C32×C29 ⋊ Dic7 |
| Hall | C7×C29 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ Dic7×C29 |
| Sylow | C7 ⋊ C29×C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | C3⋊D21 |
| commutator, hypocenter | C32×C7 | C4×C29 |
| Frattini | C2 | C29×C3⋊D21 |
| Fitting, socle | C2×C32×C7×C29 | C2 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C2×C29 | |
72 conjugacy classes of subgroups.
1914 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C29×C3⋊Dic105, C5×C29×C3⋊Dic21, C29×C3⋊(C3⋊(C7⋊AGL(1,𝔽5))) |
| maximal normal subgroup of | C5×C29×C3⋊Dic21 |
| maximal quotient of | C29×C3⋊Dic105, C5×C29×C3⋊Dic21, C29×C3⋊(C3⋊(C7⋊AGL(1,𝔽5))) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 77);