Finite Group Databasebeta

← Prev (#37560993) Next (#37560995) →

C9×C7⋊(C19⋊AGL(1,𝔽5)) #37560994

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

Aliases

direct productC9×C7⋊(C19⋊AGL(1,𝔽5))

Splittings

Fitting, HallC5×C7×C9×C19 ⋊ C4
derived, HallC5×C7×C19 ⋊ C4×C9
HallC7×C9×C19 ⋊ AGL(1,𝔽5)
HallC5×C9×C19 ⋊ Dic7
HallC5×C7×C9 ⋊ Dic19
HallC9×C19 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C19 ⋊ C9×AGL(1,𝔽5)
HallC5×C19 ⋊ C9×Dic7
HallC7×C9 ⋊ C19⋊AGL(1,𝔽5)
HallC5×C9 ⋊ Dic133
HallC5×C7 ⋊ C9×Dic19
SylowC19 ⋊ C9×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C9×C19⋊AGL(1,𝔽5)
SylowC5 ⋊ C9×Dic133

Subgroups

subgroupG/H
center, hypercenterC9C7⋊(C19⋊AGL(1,𝔽5))
commutator, hypocenterC5×C7×C19C4×C9
FrattiniC3C3×C7⋊(C19⋊AGL(1,𝔽5))
FittingC5×C7×C9×C19C4
socleC3×C5×C7×C19C3×C4
prime radical, cosocleC3×C7×D5×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5985

Conjugacy classes & character table

2421 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 126);