Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C112 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11757246 |
| commutator, Fitting, cosocle | C4×C112 | C22 |
| Frattini, hypercenter | C4 | D112 |
| socle | C2×C112 | D4 |
| hypocenter | C112 | D8 |
| LCS | G ▷ C4×C112 ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C2 ◁ C4 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^4,11^2|b^2=cd,c^2=d,b^a=bc,c^a=cd,f^a=f^10,e^b=e^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #72222561, #72222601, #72222607, … |
| maximal normal subgroup of | #72222561, #72222601, #72222607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 52);