Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D43)⋊C8 |
| Fitting | C2×C8×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 688 |
Polycyclic presentation:
2^5,43|a^2=d,d^2=e,b^a=bc,f^b=f^42356 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C8×D43, C2×(C2×D43)⋊C8, #14582861, … |
| maximal normal subgroup of | C22⋊C8×D43, C2×(C2×D43)⋊C8, #14582861, … |
| maximal quotient of | #14582622, #14582624, #14582626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 58);