Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C53 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #6157 |
| commutator, hypocenter | C53 | C32 |
| Fitting | C8×C53 | C4 |
| socle, prime radical | C2×C53 | C16 |
| cosocle | #11719908 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^5,53|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^30,f^b=f^52136 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13133267, D53⋊C32, #16811555, … |
| maximal normal subgroup of | C2×#13133267, D53⋊C32, #16811555, … |
| maximal quotient of | #16811462, C2×#13133267 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 196);