Finite Group Databasebeta

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D7×C17×AGL(1,𝔽11) #39910409

order26180
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productD7×C17×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D7×C17)
unambiguous semidirect product(D7×D11)⋊(C5×C17)
unambiguous semidirect product(C7×AGL(1,𝔽11))⋊(C2×C17)
unambiguous semidirect product(D7×C11⋊C5)⋊(C2×C17)
unambiguous semidirect product(C7⋊AGL(1,𝔽11))⋊(C2×C17)
unambiguous semidirect product(D7×C17×D11)⋊C5

Splittings

Fitting, socle, HallC7×C11×C17 ⋊ C22×C5
derived, HallC7×C11 ⋊ C22×C5×C17
HallC7×C17×C11⋊C5 ⋊ C22
HallD7×C17×D11 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×D7
HallC7×C11⋊C5 ⋊ C22×C17
HallD7×D11 ⋊ C5×C17
HallC11×C17 ⋊ C2×C5×D7
HallC7×C17 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D7×C17
SylowC11 ⋊ C2×C5×D7×C17
SylowC7 ⋊ C2×C17×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC17D7×AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C22×C5×C17
FrattiniC1G
Fitting, socleC7×C11×C17C22×C5
LCSG ▷ C7×C11
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1309

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 31);