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C5×#14523823⋊C3 #44544345

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#14523823⋊C3
unambiguous semidirect product(C5×#14523823)⋊C3

Splittings

Fitting, socle, HallC5×C13×C41 ⋊ C3×C4
derived, HallC13×C41 ⋊ C3×C4×C5
HallC5×#14523823 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C4
Hall#14523823 ⋊ C3×C5
HallC13⋊C3×C41 ⋊ C4×C5
HallC5×C41 ⋊ AGL(1,𝔽13)
HallC5×C13⋊C3 ⋊ Dic41
HallC5×C13 ⋊ C3×Dic41
SylowC41 ⋊ C5×AGL(1,𝔽13)
HallC13⋊C3 ⋊ C5×Dic41
SylowC13 ⋊ C3×C5×Dic41

Subgroups

subgroupG/H
center, hypercenterC5#14523823⋊C3
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC1G
Fitting, socleC5×C13×C41C3×C4
prime radicalC5×C41×D13⋊C3C2
cosocleD13×C41C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 73);