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AGL(1,𝔽7)×D95 #22547658

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

Aliases

direct productAGL(1,𝔽7)×D95
unambiguous semidirect productD7⋊(C3×D95)
unambiguous semidirect product(C5×AGL(1,𝔽7))⋊D19
unambiguous semidirect product(C19×AGL(1,𝔽7))⋊D5

Splittings

Fitting, socle, derived, HallC5×C7×C19 ⋊ C22×C3
HallD7×D95 ⋊ 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) ⋊ C2×D95
SylowC19 ⋊ D5×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D95
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

343 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×C5⋊(D19⋊C3), C3×AGL(1,𝔽7)×D95, AGL(1,𝔽7)×D285, …
maximal normal subgroup ofAGL(1,𝔽7)×C5⋊(D19⋊C3), C3×AGL(1,𝔽7)×D95
maximal quotient ofD7⋊C9×D95, C3×AGL(1,𝔽7)×D95, AGL(1,𝔽7)×D285, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 83);