Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D53 |
| commutator, socle, cosocle | C2×C53 | C24 |
| Fitting | C2×Q8×C53 | C2 |
| hypercenter | C2×Q8 | D53 |
| hypocenter | C53 | 2−1+4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^5,53|b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,f^b=f^52,f^d=f^52277 conjugacy classes — view the full character table.
| maximal subgroup of | #16810795, #16810798, #16810805, … |
| maximal normal subgroup of | #16810795, #16810798, #16810805, … |
| maximal quotient of | #16811099, #16811101, #16811104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 194);