Finite Group Databasebeta

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C41×C3⋊#63118 #44544457

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

Aliases

direct productC41×C3⋊#63118
unambiguous semidirect productC3⋊(C41×#63118)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C4
derived, HallC3×C5×C13 ⋊ C4×C41
HallC5×C13×C41 ⋊ Dic3
HallC3×C13×C41 ⋊ Dic5
HallC3×C5×C41 ⋊ #261
HallC13×C41 ⋊ Dic15
HallC5×C41 ⋊ C3⋊#261
HallC3×C41 ⋊ #63118
HallC5×C13 ⋊ Dic3×C41
HallC3×C13 ⋊ Dic5×C41
HallC3×C5 ⋊ C41×#261
SylowC13 ⋊ C41×Dic15
SylowC5 ⋊ C41×C3⋊#261
SylowC3 ⋊ C41×#63118

Subgroups

subgroupG/H
center, hypercenterC41C3⋊#63118
commutator, hypocenterC3×C5×C13C4×C41
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×C5×D13×C41C2
cosocleC3×C5×D13C2×C41
LCSG ▷ C3×C5×C13
UCSC1 ◁ C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

2583 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 185);