Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C271 ⋊ C2 |
| Sylow | C271 ⋊ #436 |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^270,c^b=cf,g^b=g^2704348 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46834321, #46834323, #46835193, … |
| maximal normal subgroup of | #46834321, #46834323, #46835193, … |
| maximal quotient of | #46835250, #46835256, #46835262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 628);