Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| 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^40,c^b=ce214 conjugacy classes — view the full character table.
| maximal subgroup of | #104×D41, C2×#13050091, #14580351, … |
| maximal normal subgroup of | #104×D41, C2×#13050091, #14580351, … |
| maximal quotient of | D4⋊#66491, Q8⋊#66491, #14580070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 73);