Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C41 ⋊ C2 |
| Sylow | C41 ⋊ #137 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^5,41|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^c=f^40151 conjugacy classes — view the full character table.
| maximal subgroup of | #137×D41, C2×#13050193, #14581132, … |
| maximal normal subgroup of | #137×D41, C2×#13050193, #14581132, … |
| maximal quotient of | #14580334, #14580343, #14580375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 175);