Finite Group Databasebeta

← Prev (#30630543) Next (#30630545) →

C41×C5⋊(D13⋊C3) #30630544

order15990
isoclinismisoclinic class of C5⋊(D13⋊C3)
automorphism?
homologyAbelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×C5⋊(D13⋊C3)
unambiguous semidirect productC5⋊(C41×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(D5×C41)
unambiguous semidirect productD65⋊(C3×C41)
unambiguous semidirect product(C41×D65)⋊C3

Splittings

Fitting, socle, HallC5×C13×C41 ⋊ C2×C3
derived, HallC5×C13 ⋊ C2×C3×C41
HallC5×C13⋊C3×C41 ⋊ C2
HallC41×D65 ⋊ C3
HallC13⋊C3×C41 ⋊ D5
HallC13×C41 ⋊ C3×D5
HallC5×C41 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ C2×C41
HallD65 ⋊ C3×C41
HallC13⋊C3 ⋊ D5×C41
SylowC13 ⋊ C3×D5×C41
SylowC5 ⋊ C41×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC41C5⋊(D13⋊C3)
commutator, cosocle, hypocenterC5×C13C2×C3×C41
FrattiniC1G
Fitting, socleC5×C13×C41C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC41×#63122⋊C3, #24922521⋊C3, C41×#63121⋊C3, …
maximal normal subgroup ofC41×#63122⋊C3, #24922521⋊C3, C41×#63121⋊C3, …
maximal quotient ofC41×Dic65⋊C3, C2×C41×C5⋊(D13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 32);