Finite Group DatabasebetaFinite Group Databasebeta| order | 7396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C43 |
| unambiguous semidirect product | C43⋊Dic43 |
| derived, Sylow | C432 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C43⋊D43 |
| commutator, hypocenter | C432 | C4 |
| Fitting, socle | C2×C432 | C2 |
| LCS | G ▷ C432 | |
| UCS | C1 ◁ C2 | |
138 conjugacy classes of subgroups.
Polycyclic presentation:
2,43^2,2|a^2=d,b^a=b^42,c^a=c^421852 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C43⋊C3)⋊Dic43, #36370804, #36370805, … |
| maximal normal subgroup of | (C43⋊C3)⋊Dic43, #36370804, #36370805, … |
| maximal quotient of | C3×C43⋊Dic43, C3⋊(C43⋊Dic43), C43⋊Dic215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7396, 7);