Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C41 ⋊ C4 |
| Sylow | C41 ⋊ #106 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^5,41|a^2=d,b^2=c,c^2=e,b^a=bc,c^a=ce,f^a=f^32,f^d=f^4094 conjugacy classes — view the full character table.
| maximal subgroup of | #14581252, #14581253, #14581260, … |
| maximal normal subgroup of | #14581252, #14581253, #14581260, … |
| maximal quotient of | #14581197, #14581198, #14581210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 214);