Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| isoclinism | isoclinic class of Dic106 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic106 |
| Sylow | C53 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D53 |
| commutator | C2×C53 | C22×C4 |
| Frattini | C22 | C22×D53 |
| Fitting | C42×C53 | C2 |
| socle, prime radical, cosocle | C22×C53 | C23 |
| hypercenter | C42 | D53 |
| hypocenter | C53 | C4×Q8 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
436 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16810353, #16810355, C4×#11719923, … |
| maximal normal subgroup of | #16810353, #16810355, C4×#11719923, … |
| maximal quotient of | C4×C4⋊Dic53, C4×#11719919, #16810506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 112);