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C2×C5⋊(C17⋊AGL(1,𝔽11)) #34035206

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

Aliases

direct productC2×C5⋊(C17⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C5)⋊(C17⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C17)⋊(C5⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊D85
unambiguous semidirect product(C2×D935)⋊C5

Splittings

Fitting, socleC2×C5×C11×C17 ⋊ C2×C5
derivedC5×C11×C17 ⋊ C22×C5
HallC5×C17×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C2×D17
HallC11×C17 ⋊ C2×C5×D5
SylowC17 ⋊ C2×C5⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D85

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C17⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC5×C11×C17C22×C5
FrattiniC1G
Fitting, socleC2×C5×C11×C17C2×C5
LCSG ▷ C5×C11×C17
UCSC1 ◁ C2

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1870

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 91);