Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C41 ⋊ #108 |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^5,41|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^32,f^b=f^40,f^d=f^4094 conjugacy classes — view the full character table.
| maximal subgroup of | #14581250, #14581251, #14581264, … |
| maximal normal subgroup of | #14581250, #14581251, #14581264, … |
| maximal quotient of | #14581198, #14581199, #14581212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 217);