Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C4×C41 ⋊ C4 |
| Sylow | C41 ⋊ #117 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^5,41|a^2=e,c^2=d,b^a=bd,f^a=f^32,f^e=f^40100 conjugacy classes — view the full character table.
| maximal subgroup of | #14581203, #14581204, #14581207, … |
| maximal normal subgroup of | #14581203, #14581204, #14581207, … |
| maximal quotient of | #14581272, C4×C22⋊#4223, C4×C4⋊#4223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 225);