Finite Group DatabasebetaFinite Group Databasebeta| order | 1136 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D71)⋊C4 |
| Fitting | C2×C4×C71 ⋊ C2 |
| Sylow | C71 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D71 |
| commutator | C2×C71 | C2×C4 |
| Fitting | C2×C4×C71 | C2 |
| socle, cosocle | C22×C71 | C22 |
| prime radical | C22×D71 | C2 |
| hypercenter | C2×C4 | D71 |
| hypocenter | C71 | C22⋊C4 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 568 |
Polycyclic presentation:
2^4,71|a^2=d,b^a=bc,e^b=e^70290 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D71, C2×(C2×D71)⋊C4, #14556085, … |
| maximal normal subgroup of | C22⋊C4×D71, C2×(C2×D71)⋊C4, #14556085, … |
| maximal quotient of | C71⋊#95, (C2×D71)⋊C8, #14556042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1136, 17);