Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C41 ⋊ C2 |
| Sylow | C41 ⋊ #137 |
60 conjugacy classes of subgroups.
| 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,f^a=f^40,d^b=de211 conjugacy classes — view the full character table.
| maximal subgroup of | #14580512, #14580513, #14580517, … |
| maximal normal subgroup of | #14580512, #14580513, #14580517, … |
| maximal quotient of | #14580335, #14580345, #14580376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 177);