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C2×AGL(1,𝔽7)×C11⋊C5 #17987643

order4620
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,𝔽7)×C11⋊C5
unambiguous semidirect productD7⋊(C2×C3×C11⋊C5)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C11⋊C5)
unambiguous semidirect product(C2×D7)⋊(C3×C11⋊C5)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C11⋊C5)
unambiguous semidirect product(C2×C11×AGL(1,𝔽7))⋊C5
unambiguous semidirect product(C2×D7×C11⋊C5)⋊C3

Splittings

Fitting, socleC2×C7×C11 ⋊ C2×C3×C5
derived, HallC7×C11 ⋊ C22×C3×C5
HallC2×D7×C11⋊C5 ⋊ C3
HallΓL(1,𝔽8)×C11⋊C5 ⋊ C22
HallC2×C11×AGL(1,𝔽7) ⋊ C5
HallC7×C11⋊C5 ⋊ C22×C3
HallC2×C11×D7 ⋊ C3×C5
HallC11×ΓL(1,𝔽8) ⋊ C22×C5
HallC2×D7 ⋊ C3×C11⋊C5
HallΓL(1,𝔽8) ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×C5×AGL(1,𝔽7)
SylowC7 ⋊ C22×C3×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽7)×C11⋊C5
commutator, cosocle, hypocenterC7×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 154

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽7)×C11⋊C5, C2×C3×AGL(1,𝔽7)×C11⋊C5, C2×C11⋊C5×C3⋊AGL(1,𝔽7), …
maximal normal subgroup ofC2×C3×AGL(1,𝔽7)×C11⋊C5, C2×C5×AGL(1,𝔽7)×C11⋊C5, C2×C7×AGL(1,𝔽7)×C11⋊C5, …
maximal quotient ofC2×C11⋊C5×D7⋊C9, D3×AGL(1,𝔽7)×C11⋊C5, C2×C3×AGL(1,𝔽7)×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 40);