Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #137 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^5,53|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^52,d^b=de,f^c=f^52193 conjugacy classes — view the full character table.
| maximal subgroup of | #137×D53, C2×#13133249, #16811420, … |
| maximal normal subgroup of | #137×D53, C2×#13133249, #16811420, … |
| maximal quotient of | #16810623, #16810630, #16810664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 178);