Finite Group Databasebeta

← Prev (#37561511) Next (#37561513) →

C32×C19×C7⋊AGL(1,𝔽5) #37561512

order23940
automorphism?
homologyAbelianization (H1) = C32×C4×C19 · Schur multiplier (H2) = C3

Aliases

direct productC32×C19×C7⋊AGL(1,𝔽5)

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C4
derived, HallC5×C7 ⋊ C32×C4×C19
HallC32×C7×C19 ⋊ AGL(1,𝔽5)
HallC32×C5×C19 ⋊ Dic7
HallC5×C7×C19 ⋊ C32×C4
HallC32×C5×C7 ⋊ C4×C19
HallC7×C19 ⋊ C32×AGL(1,𝔽5)
HallC5×C19 ⋊ C32×Dic7
HallC32×C7 ⋊ C19×AGL(1,𝔽5)
HallC32×C5 ⋊ C19×Dic7
SylowC7 ⋊ C32×C19×AGL(1,𝔽5)
SylowC5 ⋊ C32×C19×Dic7

Subgroups

subgroupG/H
center, hypercenterC32×C19C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C32×C4×C19
FrattiniC1G
Fitting, socleC32×C5×C7×C19C4
prime radicalC32×C7×D5×C19C2
cosocleC7×D5C2×C32×C19
LCSG ▷ C5×C7
UCSC1 ◁ C32×C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5985

Conjugacy classes & character table

2907 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 644);