Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^5,53|a^2=d,d^2=e,b^a=bc,f^b=f^52436 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C8×D53, C2×#13133129, #16810585, … |
| maximal normal subgroup of | C22⋊C8×D53, C2×#13133129, #16810585, … |
| maximal quotient of | #16810346, #16810348, #16810350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 58);