Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of C11⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C11⋊#170 |
| unambiguous semidirect product | (C2×C11)⋊#170 |
| derived, Hall | C5×C11 ⋊ C2×C8 |
| Sylow | C11 ⋊ C2×#170 |
| Sylow | C5 ⋊ C2×C11⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C11⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C11 | C2×C8 |
| Frattini | C2 | C2×C11⋊AGL(1,𝔽5) |
| Fitting, socle, prime radical | C22×C5×C11 | C4 |
| cosocle | C11×Dic5 | C22 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C22 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 880 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #170×Dic11, #13182577, (C2×D11)⋊#170, … |
| maximal normal subgroup of | #170×Dic11, #13182577, (C2×D11)⋊#170, … |
| maximal quotient of | C2×C11⋊#674, #13182644, C4×C11⋊#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 146);