Finite Group DatabasebetaFinite Group Databasebeta| order | 2096 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic131 |
| Sylow | C131 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D131 |
| commutator | C2×C131 | C2×C4 |
| Fitting, prime radical | C23×C131 | C2 |
| socle, cosocle | C22×C131 | C22 |
| hypercenter | C23 | D131 |
| hypocenter | C131 | C22⋊C4 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C22 ◁ C23 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1048 |
Polycyclic presentation:
2^4,131|a^2=d,b^a=bc,e^a=e^130530 conjugacy classes — view the full character table.
| maximal subgroup of | #16862160, #16862161, C22⋊C4×D131, … |
| maximal normal subgroup of | #16862160, #16862161, C22⋊C4×D131, … |
| maximal quotient of | C131⋊#95, C22⋊(C131⋊C8), #16862161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2096, 18);