Finite Group Databasebeta

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C3×C47×#63120 #49144041

order36660
automorphism?
homologyAbelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productC3×C47×#63120

Splittings

Fitting, socle, HallC3×C5×C13×C47 ⋊ C4
derived, HallC5×C13 ⋊ C3×C4×C47
HallC5×C13×C47 ⋊ C3×C4
HallC3×C13×C47 ⋊ AGL(1,𝔽5)
HallC3×C5×C47 ⋊ Dic13
HallC13×C47 ⋊ C3×AGL(1,𝔽5)
HallC5×C47 ⋊ C3×Dic13
HallC3×C5×C13 ⋊ C4×C47
HallC3×C13 ⋊ AGL(1,𝔽5)×C47
HallC3×C5 ⋊ C47×Dic13
SylowC13 ⋊ C3×AGL(1,𝔽5)×C47
SylowC5 ⋊ C3×C47×Dic13

Subgroups

subgroupG/H
center, hypercenterC3×C47#63120
commutator, hypocenterC5×C13C3×C4×C47
FrattiniC1G
Fitting, socleC3×C5×C13×C47C4
prime radicalC3×D5×C13×C47C2
cosocleD5×C13C2×C3×C47
LCSG ▷ C5×C13
UCSC1 ◁ C3×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9165

Conjugacy classes & character table

4089 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36660, 61);