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C2×C5⋊(C7⋊AGL(1,𝔽11)) #21440410

order7700
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(C7⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C5)⋊(C7⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C7)⋊(C5⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊D35
unambiguous semidirect product(C2×D385)⋊C5

Splittings

Fitting, socleC2×C5×C7×C11 ⋊ C2×C5
derivedC5×C7×C11 ⋊ C22×C5
HallC5×C7×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C2×D7
HallC7×C11 ⋊ C2×C5×D5
SylowC11 ⋊ C2×C5×D35
SylowC7 ⋊ C2×C5⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C7⋊AGL(1,𝔽11))
commutator, hypocenterC5×C7×C11C22×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C11C2×C5
LCSG ▷ C5×C7×C11
UCSC1 ◁ C2

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11)), D3×C5⋊(C7⋊AGL(1,𝔽11)), C2×C3×C5⋊(C7⋊AGL(1,𝔽11)), …
maximal normal subgroup ofC2×C5⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11)), C2×C3×C5⋊(C7⋊AGL(1,𝔽11))
maximal quotient ofD3×C5⋊(C7⋊AGL(1,𝔽11)), C2×C3×C5⋊(C7⋊AGL(1,𝔽11)), C2×C3⋊(C5⋊(C7⋊AGL(1,𝔽11)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 74);