Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#6157 |
| commutator, socle | C2×C53 | C22×C4 |
| Fitting | D4×C53 | C4 |
| prime radical | #11719947 | C2 |
| cosocle | Dic53 | C23 |
| hypercenter | D4 | #6157 |
| hypocenter | C53 | #131 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ D4 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^5,53|a^2=d,d^2=e,f^a=f^30,c^b=ce,f^d=f^5285 conjugacy classes — view the full character table.
| maximal subgroup of | #16811665, #16811666, #16811668, … |
| maximal normal subgroup of | #16811665, #16811666, #16811668, … |
| maximal quotient of | #16811587, #16811588, #16811596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 233);