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C3×C41×#63121 #44544407

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

Aliases

direct productC3×C41×#63121

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C41#63121
commutator, hypocenterC5×C13C3×C4×C41
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×C41×D65C2
cosocleD65C2×C3×C41
LCSG ▷ C5×C13
UCSC1 ◁ C3×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

2460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 135);