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C3×C13×#11717961 #44544400

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×#11717961

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C4
derived, HallC5×C41 ⋊ C3×C4×C13
HallC5×C13×C41 ⋊ C3×C4
HallC3×C13×C41 ⋊ AGL(1,𝔽5)
HallC3×C5×C41 ⋊ C4×C13
HallC13×C41 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C13 ⋊ #4223
HallC3×C41 ⋊ C13×AGL(1,𝔽5)
HallC5×C13 ⋊ C3×#4223
SylowC41 ⋊ C3×C13×AGL(1,𝔽5)
HallC3×C5 ⋊ C13×#4223
SylowC5 ⋊ C3×C13×#4223

Subgroups

subgroupG/H
center, hypercenterC3×C13#11717961
commutator, hypocenterC5×C41C3×C4×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×C13×D205C2
cosocleD205C2×C3×C13
LCSG ▷ C5×C41
UCSC1 ◁ C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 128);