Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D53 |
| commutator | C2×C53 | C42 |
| Fitting | C22×C4×C53 | C2 |
| socle, prime radical, cosocle | C23×C53 | C22 |
| hypercenter | C22×C4 | D53 |
| hypocenter | C53 | #95 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^5,53|a^2=d,b^2=e,b^a=bc,f^b=f^52436 conjugacy classes — view the full character table.
| maximal subgroup of | #16810357, #16810358, #16810360, … |
| maximal normal subgroup of | #16810357, #16810358, #16810360, … |
| maximal quotient of | #16810377, #16810378, #16810379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 53);