Finite Group DatabasebetaFinite Group Databasebeta| order | 3698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C43 |
| unambiguous semidirect product | C43⋊D43 |
| Fitting, socle, derived, Sylow | C432 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C432 | C2 |
| LCS | G ▷ C432 | |
| UCS | C1 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1849 |
Polycyclic presentation:
2,43^2|b^a=b^42,c^a=c^42926 conjugacy classes — view the full character table.
| maximal subgroup of | (C43⋊C3)⋊D43, #26012697, #26012698, … |
| maximal normal subgroup of | (C43⋊C3)⋊D43, #26012697, #26012698, … |
| maximal quotient of | C3×C43⋊D43, C3⋊(C43⋊D43), C5⋊(C43⋊D43), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3698, 4);