Finite Group Databasebeta

← Prev (#49185778) Next (#49185780) →

C3×(C41⋊C5)⋊D31 #49185779

order38130
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C41⋊C5)⋊D31
unambiguous semidirect product(C41⋊C5)⋊(C3×D31)

Splittings

Fitting, socle, HallC3×C31×C41 ⋊ C2×C5
derived, HallC31×C41 ⋊ C2×C3×C5
HallC3×C31×C41⋊C5 ⋊ C2
HallC3×D1271 ⋊ C5
HallC31×C41⋊C5 ⋊ C2×C3
HallD1271 ⋊ C3×C5
HallC3×C41⋊C5 ⋊ D31
HallC41⋊C5 ⋊ C3×D31
HallC3×C41 ⋊ C5×D31
HallC3×C31 ⋊ D41⋊C5
SylowC41 ⋊ C3×C5×D31
SylowC31 ⋊ C3×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC3(C41⋊C5)⋊D31
commutator, cosocle, hypocenterC31×C41C2×C3×C5
FrattiniC1G
Fitting, socleC3×C31×C41C2×C5
LCSG ▷ C31×C41
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3813

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38130, 42);