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D19×C5⋊AGL(1,𝔽7) #22547648

order7980
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD19×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(ΓL(1,𝔽8)×D19)⋊D5

Splittings

Fitting, socle, derived, HallC5×C7×C19 ⋊ C22×C3
HallD19×D35 ⋊ C3
HallC5×C19×ΓL(1,𝔽8) ⋊ C22
HallC19×ΓL(1,𝔽8) ⋊ C2×D5
HallC7×C19 ⋊ C2×C3×D5
HallC5×ΓL(1,𝔽8) ⋊ C2×D19
HallC5×C19 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D19
HallΓL(1,𝔽8) ⋊ D5×D19
SylowC19 ⋊ C2×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×D5×D19
SylowC5 ⋊ D19×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C19C22×C3
LCSG ▷ C5×C7×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

187 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19⋊C3×C5⋊AGL(1,𝔽7), C3×D19×C5⋊AGL(1,𝔽7), D19×C3⋊(C5⋊AGL(1,𝔽7)), …
maximal normal subgroup ofD19⋊C3×C5⋊AGL(1,𝔽7), C3×D19×C5⋊AGL(1,𝔽7)
maximal quotient ofD19×C5⋊(D7⋊C9), C3×D19×C5⋊AGL(1,𝔽7), D19×C3⋊(C5⋊AGL(1,𝔽7)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 73);