Finite Group DatabasebetaFinite Group Databasebeta| order | 1136 |
| isoclinism | isoclinic class of D71 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic71 |
| unambiguous semidirect product | C71⋊C42 |
| derived, Sylow | C71 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D71 |
| commutator, hypocenter | C71 | C42 |
| Frattini | C22 | C2×D71 |
| Fitting | C2×C4×C71 | C2 |
| socle, prime radical, cosocle | C22×C71 | C22 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic71, #14556038, #14556054, … |
| maximal normal subgroup of | C8×Dic71, #14556038, #14556054, … |
| maximal quotient of | C71⋊#95, C8×Dic71, C4×C71⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1136, 16);