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AGL(1,𝔽7)×D55 #17987662

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

Aliases

direct productAGL(1,𝔽7)×D55
unambiguous semidirect productD7⋊(C3×D55)
unambiguous semidirect product(C5×AGL(1,𝔽7))⋊D11
unambiguous semidirect product(C11×AGL(1,𝔽7))⋊D5
unambiguous semidirect product(D7×D55)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C11 ⋊ C22×C3
HallD7×D55 ⋊ C3
HallC5×C11×ΓL(1,𝔽8) ⋊ C22
HallC11×ΓL(1,𝔽8) ⋊ C2×D5
HallC5×ΓL(1,𝔽8) ⋊ C2×D11
HallC7×C11 ⋊ C2×C3×D5
HallC5×C11 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D11
HallΓL(1,𝔽8) ⋊ C2×D55
SylowC11 ⋊ D5×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D55
SylowC5 ⋊ D11×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C11C22×C3
LCSG ▷ C5×C7×C11
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 385

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×D55, AGL(1,𝔽7)×D165, D55×C3⋊AGL(1,𝔽7), …
maximal normal subgroup ofC3×AGL(1,𝔽7)×D55, AGL(1,𝔽7)×C5⋊AGL(1,𝔽11), C5×AGL(1,𝔽7)×D55, …
maximal quotient ofD55×D7⋊C9, C3×AGL(1,𝔽7)×D55, AGL(1,𝔽7)×D165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 59);