Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of C11⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×C11⋊AGL(1,𝔽5) |
| Fitting | C4×C5×C11 ⋊ C4 |
| derived, Hall | C5×C11 ⋊ C42 |
| Sylow | C11 ⋊ C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C11⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C11 | C42 |
| Frattini | C2 | C2×C11⋊AGL(1,𝔽5) |
| Fitting | C4×C5×C11 | C4 |
| socle | C2×C5×C11 | C2×C4 |
| prime radical, cosocle | C2×D5×C11 | C22 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | (C11⋊AGL(1,𝔽5))⋊C8, #13182558, #13182563, … |
| maximal normal subgroup of | (C11⋊AGL(1,𝔽5))⋊C8, #13182558, #13182563, … |
| maximal quotient of | C8×C11⋊AGL(1,𝔽5), #13182638, C4×C11⋊#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 144);