Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #97×C271 ⋊ C2 |
| Sylow | C271 ⋊ #433 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^270,c^b=cf,g^b=g^2702728 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #433×D271, C2×#31773959, #46844998, … |
| maximal normal subgroup of | #433×D271, C2×#31773959, #46844998, … |
| maximal quotient of | #46836117, #46836133, #46836224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 611);