Finite Group Databasebeta

← Prev (#34089493) Next (#34089495) →

C3×C47×C7⋊AGL(1,𝔽5) #34089494

order19740
automorphism?
homologyAbelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productC3×C47×C7⋊AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C7×C47 ⋊ C4
derived, HallC5×C7 ⋊ C3×C4×C47
HallC5×C7×C47 ⋊ C3×C4
HallC3×C7×C47 ⋊ AGL(1,𝔽5)
HallC3×C5×C47 ⋊ Dic7
HallC7×C47 ⋊ C3×AGL(1,𝔽5)
HallC5×C47 ⋊ C3×Dic7
HallC3×C5×C7 ⋊ C4×C47
HallC3×C7 ⋊ AGL(1,𝔽5)×C47
HallC3×C5 ⋊ Dic7×C47
SylowC7 ⋊ C3×AGL(1,𝔽5)×C47
SylowC5 ⋊ C3×Dic7×C47

Subgroups

subgroupG/H
center, hypercenterC3×C47C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C3×C4×C47
FrattiniC1G
Fitting, socleC3×C5×C7×C47C4
prime radicalC3×C7×D5×C47C2
cosocleC7×D5C2×C3×C47
LCSG ▷ C5×C7
UCSC1 ◁ C3×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4935

Conjugacy classes & character table

2397 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 47);