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C19×(C7⋊C9)⋊AGL(1,𝔽5) #37560924

order23940
automorphism?
homologyAbelianization (H1) = C4×C9×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×(C7⋊C9)⋊AGL(1,𝔽5)
unambiguous semidirect product(C7⋊C9)⋊(C19×AGL(1,𝔽5))
unambiguous semidirect product(C7⋊AGL(1,𝔽5))⋊(C9×C19)

Splittings

derived, HallC5×C7 ⋊ C4×C9×C19
HallC5×C19×C7⋊C9 ⋊ C4
HallC19×C7⋊AGL(1,𝔽5) ⋊ C9
HallC19×C7⋊C9 ⋊ AGL(1,𝔽5)
HallC5×C7×C19 ⋊ C4×C9
HallC5×C7⋊C9 ⋊ C4×C19
HallC7⋊AGL(1,𝔽5) ⋊ C9×C19
HallC7×C19 ⋊ C9×AGL(1,𝔽5)
HallC5×C19 ⋊ Dic7⋊C9
HallC7⋊C9 ⋊ C19×AGL(1,𝔽5)
SylowC7 ⋊ C9×C19×AGL(1,𝔽5)
SylowC5 ⋊ C19×Dic7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C19ΓL(1,𝔽8)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C9×C19
FrattiniC3C19×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
Fitting, socleC3×C5×C7×C19C3×C4
prime radicalC3×C7×D5×C19C2×C3
cosocleC3×C7×D5C2×C3×C19
LCSG ▷ C5×C7
UCSC1 ◁ C3×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5985

Conjugacy classes & character table

1083 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 56);