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C41×C3⋊#63120 #44544451

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

Aliases

direct productC41×C3⋊#63120
unambiguous semidirect productC3⋊(C41×#63120)

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 ⋊ Dic13
HallC13×C41 ⋊ ΓL(1,𝔽16)
HallC5×C41 ⋊ Dic39
HallC3×C41 ⋊ #63120
HallC5×C13 ⋊ Dic3×C41
HallC3×C13 ⋊ AGL(1,𝔽5)×C41
HallC3×C5 ⋊ C41×Dic13
SylowC13 ⋊ C41×ΓL(1,𝔽16)
SylowC5 ⋊ C41×Dic39
SylowC3 ⋊ C41×#63120

Subgroups

subgroupG/H
center, hypercenterC41C3⋊#63120
commutator, hypocenterC3×C5×C13C4×C41
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×D5×C13×C41C2
cosocleC3×D5×C13C2×C41
LCSG ▷ C3×C5×C13
UCSC1 ◁ C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

3321 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 179);