Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C5×C11 ⋊ C2×C8 |
| Sylow | C11 ⋊ D5⋊C8 |
| Sylow | C5 ⋊ C8×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×D11 |
| commutator, hypocenter | C5×C11 | C2×C8 |
| Fitting, socle | C2×C5×C11 | C2×C4 |
| prime radical | C2×D55 | C4 |
| cosocle | C11×Dic5 | C22 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 440 |
Polycyclic presentation:
2^4,5,11|a^2=d,b^2=c,c^2=d,f^a=f^10,e^b=e^2,e^c=e^470 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D5⋊C8, #13183300, #13183301, … |
| maximal normal subgroup of | D11×D5⋊C8, #13183300, #13183301, … |
| maximal quotient of | #13182572, #13182574, #170×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 128);