Finite Group DatabasebetaFinite Group Databasebeta| order | 6724 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D412 |
| unambiguous semidirect product | (C41×D41)⋊C2 |
| unambiguous semidirect product | (C41⋊D41)⋊C2 |
| Fitting, socle, derived, Sylow | C412 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C412 | C22 |
| LCS | G ▷ C412 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
484 conjugacy classes — view the full character table.
| maximal subgroup of | #23758624⋊C2, C3×D412, D41×D123, … |
| maximal normal subgroup of | C3×D412, D41×D41⋊C5, #30681140⋊C2, … |
| maximal quotient of | C3×D412, D41×D123, D123⋊D41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6724, 12);