Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×#6157 |
| Fitting | Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#6157 |
| commutator, socle | C2×C53 | C22×C4 |
| Fitting | Q8×C53 | C4 |
| prime radical, cosocle | C2×D53 | C23 |
| hypercenter | Q8 | #6157 |
| hypocenter | C53 | C4×Q8 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#6157, Q16×#6157, #16811662, … |
| maximal normal subgroup of | SD16×#6157, Q16×#6157, #16811662, … |
| maximal quotient of | C4⋊C4×#6157, #16811572, #16811574, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 227);