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C7×(C19⋊C3)⋊AGL(1,𝔽5) #22547629

order7980
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×(C19⋊C3)⋊AGL(1,𝔽5)
unambiguous semidirect product(C19⋊C3)⋊(C7×AGL(1,𝔽5))
unambiguous semidirect product(C19⋊AGL(1,𝔽5))⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C19 ⋊ C3×C4
derived, HallC5×C19 ⋊ C3×C4×C7
HallC7×C19⋊AGL(1,𝔽5) ⋊ C3
HallC5×C7×C19⋊C3 ⋊ C4
HallC7×C19⋊C3 ⋊ AGL(1,𝔽5)
HallC19⋊AGL(1,𝔽5) ⋊ C3×C7
HallC5×C19⋊C3 ⋊ C4×C7
HallC7×C19 ⋊ C3×AGL(1,𝔽5)
HallC19⋊C3 ⋊ C7×AGL(1,𝔽5)
HallC5×C7 ⋊ (C19⋊C3)⋊C4
SylowC19 ⋊ C3×C7×AGL(1,𝔽5)
SylowC5 ⋊ C7×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC7(C19⋊C3)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C19C3×C4×C7
FrattiniC1G
Fitting, socleC5×C7×C19C3×C4
LCSG ▷ C5×C19
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×#4296⋊AGL(1,𝔽5), #37561190, #37561191, …
maximal normal subgroup ofC7×#4296⋊AGL(1,𝔽5), #37561190, #37561191, …
maximal quotient ofC7×#4294⋊AGL(1,𝔽5), C3×C7×(C19⋊C3)⋊AGL(1,𝔽5), C7×C3⋊((C19⋊C3)⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 54);