Finite Group DatabasebetaFinite Group Databasebeta| order | 2272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C71 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D71 |
| commutator, socle, cosocle | C22×C71 | C23 |
| Fitting | C22⋊C4×C71 | C2 |
| prime radical | C23×C71 | C22 |
| hypercenter | C22⋊C4 | D71 |
| hypocenter | C71 | #126 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^5,71|b^2=de,c^2=d,b^a=bd,c^a=ce,f^c=f^70364 conjugacy classes — view the full character table.
| maximal subgroup of | #126×D71, C2×#14556121, #17986526, … |
| maximal normal subgroup of | #126×D71, C2×#14556121, #17986526, … |
| maximal quotient of | #17985866, #17985881, #17985884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2272, 139);