Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C41 ⋊ C4 |
| Sylow | C41 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^5,41|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^32,c^b=ce,f^b=f^40,f^d=f^4064 conjugacy classes — view the full character table.
| maximal subgroup of | D41⋊#104, C2×#13050229, #14581333, … |
| maximal normal subgroup of | D41⋊#104, C2×#13050229, #14581333, … |
| maximal quotient of | #14581184, Q8⋊#66493, #14581188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 211);