Finite Group Databasebeta

← Prev (#44544446) Next (#44544448) →

C41×C3⋊#63121 #44544447

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

Aliases

direct productC41×C3⋊#63121
unambiguous semidirect productC3⋊(C41×#63121)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C4
derived, HallC3×C5×C13 ⋊ C4×C41
HallC5×C13×C41 ⋊ Dic3
HallC3×C13×C41 ⋊ AGL(1,𝔽5)
HallC3×C5×C41 ⋊ #261
HallC13×C41 ⋊ ΓL(1,𝔽16)
HallC5×C41 ⋊ C3⋊#261
HallC3×C41 ⋊ #63121
HallC5×C13 ⋊ Dic3×C41
HallC3×C13 ⋊ AGL(1,𝔽5)×C41
HallC3×C5 ⋊ C41×#261
SylowC13 ⋊ C41×ΓL(1,𝔽16)
SylowC5 ⋊ C41×C3⋊#261
SylowC3 ⋊ C41×#63121

Subgroups

subgroupG/H
center, hypercenterC41C3⋊#63121
commutator, hypocenterC3×C5×C13C4×C41
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×C41×D65C2
cosocleC3×D65C2×C41
LCSG ▷ C3×C5×C13
UCSC1 ◁ C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

2214 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 175);