Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C11 |
No aliases for this group.
| Fitting | C2×C4×C112 ⋊ C2 |
| Sylow | C112 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×C11⋊D11 |
| commutator, socle, cosocle | C2×C112 | C23 |
| Frattini | C2 | C22×C11⋊D11 |
| Fitting | C2×C4×C112 | C2 |
| hypercenter | C2×C4 | C11⋊D11 |
| hypocenter | C112 | #41 |
| LCS | G ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 968 |
Polycyclic presentation:
2^4,11^2|b^2=d,c^a=cd,e^a=e^10,f^a=f^10490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 148);