Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D43)⋊C4 |
| Fitting | C22⋊C4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 688 |
Polycyclic presentation:
2^5,43|a^2=e,c^2=e,b^a=bd,f^c=f^42230 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D4×D43, C2×(C22⋊D43)⋊C4, C4×#10621900, … |
| maximal normal subgroup of | C4×D4×D43, C2×(C22⋊D43)⋊C4, C4×#10621900, … |
| maximal quotient of | #14582746, C22⋊C4×Dic43, #14582750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 106);