Finite Group Databasebeta

← Prev (#13183337) Next (#13183339) →

D4×C11×AGL(1,𝔽5) #13183338

order1760
automorphism?
homologyAbelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23

Aliases

direct productD4×C11×AGL(1,𝔽5)

Splittings

FittingC5×D4×C11 ⋊ C4
HallC5×C11 ⋊ C4×D4
SylowC5 ⋊ C4×D4×C11

Subgroups

subgroupG/H
centerC2×C11C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C11
FrattiniC2C22×C11×AGL(1,𝔽5)
FittingC5×D4×C11C4
socleC2×C5×C11C22×C4
prime radicalD4×D5×C11C2
cosocleC2×D5C23×C11
hypercenterD4×C11AGL(1,𝔽5)
hypocenterC5C4×D4×C11
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ D4×C11

188 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 220

Conjugacy classes & character table

275 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×D11, D4×AGL(1,𝔽5)×C11⋊C5
maximal normal subgroup ofD4×AGL(1,𝔽5)×D11, D4×AGL(1,𝔽5)×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1147);