Finite Group Databasebeta

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C3×C47⋊#63118 #49144045

order36660
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C47⋊#63118
unambiguous semidirect productC47⋊(C3×#63118)

Splittings

Fitting, socle, HallC3×C5×C13×C47 ⋊ C4
derived, HallC5×C13×C47 ⋊ C3×C4
HallC3×C13×C47 ⋊ Dic5
HallC3×C5×C47 ⋊ #261
HallC13×C47 ⋊ C3×Dic5
HallC5×C47 ⋊ C3×#261
HallC3×C5×C13 ⋊ Dic47
HallC3×C47 ⋊ #63118
HallC5×C13 ⋊ C3×Dic47
SylowC47 ⋊ C3×#63118
HallC3×C13 ⋊ Dic235
HallC3×C5 ⋊ C47⋊#261
SylowC13 ⋊ C3×Dic235
SylowC5 ⋊ C3×C47⋊#261

Subgroups

subgroupG/H
center, hypercenterC3C47⋊#63118
commutator, hypocenterC5×C13×C47C3×C4
FrattiniC1G
Fitting, socleC3×C5×C13×C47C4
prime radicalC3×C5×D13×C47C2
cosocleC5×D13×C47C2×C3
LCSG ▷ C5×C13×C47
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9165

Conjugacy classes & character table

2829 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36660, 65);