Finite Group DatabasebetaFinite Group Databasebeta| order | 1136 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C71 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D71 |
| commutator, cosocle | C4×C71 | C22 |
| Frattini | C4 | C2×D71 |
| Fitting | Q8×C71 | C2 |
| socle, prime radical | C2×C71 | D4 |
| hypercenter | Q8 | D71 |
| hypocenter | C71 | Q16 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^4,71|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^70182 conjugacy classes — view the full character table.
| maximal subgroup of | Q16×D71, C2×#11765855, #14556148, … |
| maximal normal subgroup of | Q16×D71, C2×#11765855, #14556148, … |
| maximal quotient of | #14556051, #14556052, #14556061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1136, 30);