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(C19⋊C3)⋊(C7⋊AGL(1,𝔽5)) #22547643

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

Aliases

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

Splittings

Fitting, socle, derived, HallC5×C7×C19 ⋊ C3×C4
HallC7⋊(C19⋊AGL(1,𝔽5)) ⋊ C3
HallC5×C7×C19⋊C3 ⋊ C4
HallC7×C19⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C19⋊C3 ⋊ Dic7
HallC7×C19 ⋊ C3×AGL(1,𝔽5)
HallC5×C19 ⋊ C3×Dic7
HallC19⋊C3 ⋊ C7⋊AGL(1,𝔽5)
HallC5×C7 ⋊ (C19⋊C3)⋊C4
SylowC19 ⋊ C3×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ (C19⋊C3)⋊AGL(1,𝔽5)
SylowC5 ⋊ (C19⋊C3)⋊Dic7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C19C3×C4
LCSG ▷ C5×C7×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,2,5,7,19|a^2=c,d^a=d^2,e^a=e^6,f^a=f^18,f^b=f^7,d^c=d^4

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#37561184, #37561185, ΓL(1,𝔽8)⋊((C19⋊C3)⋊AGL(1,𝔽5)), …
maximal normal subgroup of#37561184, #37561185, ΓL(1,𝔽8)⋊((C19⋊C3)⋊AGL(1,𝔽5)), …
maximal quotient of#4294⋊(C7⋊AGL(1,𝔽5)), C3×(C19⋊C3)⋊(C7⋊AGL(1,𝔽5)), C3⋊((C19⋊C3)⋊(C7⋊AGL(1,𝔽5)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 68);