Finite Group DatabasebetaFinite Group Databasebeta| order | 1136 |
| isoclinism | isoclinic class of D71 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C71⋊C16 |
| derived, Sylow | C71 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D71 |
| commutator, hypocenter | C71 | C16 |
| Fitting, cosocle | C8×C71 | C2 |
| socle, prime radical | C2×C71 | C8 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^4,71|a^2=b,b^2=c,c^2=d,e^a=e^70296 conjugacy classes — view the full character table.
| maximal subgroup of | C16×D71, C2×C71⋊C16, #14556067, … |
| maximal normal subgroup of | C16×D71, C2×C71⋊C16, #14556067, … |
| maximal quotient of | C71⋊C32, C2×C71⋊C16 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1136, 15);