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C2×C17×C5⋊AGL(1,𝔽11) #34035205

order18700
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×C5⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C5)⋊(C17×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(D5×C17)
unambiguous semidirect product(C2×D55)⋊(C5×C17)
unambiguous semidirect product(C2×C17×D55)⋊C5

Splittings

Fitting, socleC2×C5×C11×C17 ⋊ C2×C5
derivedC5×C11 ⋊ C22×C5×C17
HallC5×C17×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C22×C17
HallC11×C17 ⋊ C2×C5×D5
SylowC11 ⋊ C2×C5×D5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17C5⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC5×C11C22×C5×C17
FrattiniC1G
Fitting, socleC2×C5×C11×C17C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C2×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1870

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 90);