Finite Group Databasebeta

← Prev (#44544360) Next (#44544362) →

AGL(1,𝔽5)×C13⋊C3×C41 #44544361

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C13⋊C3×C41
unambiguous semidirect product(C13×AGL(1,𝔽5))⋊(C3×C41)
unambiguous semidirect product(C13×AGL(1,𝔽5)×C41)⋊C3

Splittings

Fitting, socle, HallC5×C13×C41 ⋊ C3×C4
derived, HallC5×C13 ⋊ C3×C4×C41
HallC13×AGL(1,𝔽5)×C41 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C4
HallC13×C41 ⋊ C3×AGL(1,𝔽5)
HallC13×AGL(1,𝔽5) ⋊ C3×C41
HallC5×C41 ⋊ C4×C13⋊C3
HallC5×C13⋊C3 ⋊ C4×C41
SylowC13 ⋊ C3×AGL(1,𝔽5)×C41
SylowC5 ⋊ C4×C13⋊C3×C41

Subgroups

subgroupG/H
center, hypercenterC41AGL(1,𝔽5)×C13⋊C3
commutator, hypocenterC5×C13C3×C4×C41
FrattiniC1G
Fitting, socleC5×C13×C41C3×C4
prime radicalD5×C13⋊C3×C41C2
cosocleD5×C13C2×C3×C41
LCSG ▷ C5×C13
UCSC1 ◁ C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

1435 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 89);