Finite Group DatabasebetaFinite Group Databasebeta| order | 7396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D432 |
| unambiguous semidirect product | (C43×D43)⋊C2 |
| unambiguous semidirect product | (C43⋊D43)⋊C2 |
| Fitting, socle, derived, Sylow | C432 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C432 | C22 |
| LCS | G ▷ C432 | |
| UCS | C1 | |
62 conjugacy classes of subgroups.
529 conjugacy classes — view the full character table.
| maximal subgroup of | #26012691⋊C2, D43×D43⋊C3, #26012695⋊C2, … |
| maximal normal subgroup of | D43×D43⋊C3, #26012695⋊C2, #26012696⋊C2, … |
| maximal quotient of | C3×D432, D43×D129, D129⋊D43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7396, 10);