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C19×C3⋊(C7⋊AGL(1,𝔽5)) #22547716

order7980
isoclinismisoclinic class of C3⋊(C7⋊AGL(1,𝔽5))
automorphism?
homologyAbelianization (H1) = C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C3⋊(C7⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C19×C7⋊AGL(1,𝔽5))
unambiguous semidirect productC7⋊(C19×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C7×C19 ⋊ C4
derived, HallC3×C5×C7 ⋊ C4×C19
HallC5×C7×C19 ⋊ Dic3
HallC3×C7×C19 ⋊ AGL(1,𝔽5)
HallC3×C5×C19 ⋊ Dic7
HallC7×C19 ⋊ ΓL(1,𝔽16)
HallC5×C19 ⋊ Dic21
HallC3×C19 ⋊ C7⋊AGL(1,𝔽5)
HallC5×C7 ⋊ Dic3×C19
HallC3×C7 ⋊ C19×AGL(1,𝔽5)
HallC3×C5 ⋊ C19×Dic7
SylowC7 ⋊ C19×ΓL(1,𝔽16)
SylowC5 ⋊ C19×Dic21
SylowC3 ⋊ C19×C7⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC19C3⋊(C7⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C7C4×C19
FrattiniC1G
Fitting, socleC3×C5×C7×C19C4
LCSG ▷ C3×C5×C7
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

855 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×C7⋊(C9⋊AGL(1,𝔽5)), C19×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)), C3⋊#22547634, …
maximal normal subgroup ofC19×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)), C3⋊#22547634, C3⋊#22547635, …
maximal quotient ofC19×C7⋊(C9⋊AGL(1,𝔽5)), C3×C19×C3⋊(C7⋊AGL(1,𝔽5)), C19×C3⋊(C3⋊(C7⋊AGL(1,𝔽5)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 141);