Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C112 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D112 |
| commutator | C2×C112 | C2×C4 |
| Fitting, socle, cosocle | C22×C112 | C22 |
| prime radical | C22×C11⋊D11 | C2 |
| hypocenter | C112 | C22⋊C4 |
| LCS | G ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C22 | |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^4,11^2|a^2=d,b^2=cd,b^a=bc,f^a=f^10,e^b=e^10190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 60);