Finite Group DatabasebetaFinite Group Databasebeta| order | 1136 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C71 ⋊ C2 |
| Sylow | C71 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D71 |
| commutator, socle, cosocle | C2×C71 | C23 |
| Fitting | Q8×C71 | C2 |
| hypercenter | Q8 | D71 |
| hypocenter | C71 | #41 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 568 |
Polycyclic presentation:
2^4,71|c^2=d,b^a=bd,e^a=e^70,e^b=e^70,e^c=e^70185 conjugacy classes — view the full character table.
| maximal subgroup of | #14556149, #14556151, #14556155, … |
| maximal normal subgroup of | #14556149, #14556151, #14556155, … |
| maximal quotient of | #14556086, #14556090, Q8×Dic71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1136, 41);