Finite Group Databasebeta

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C3×D5×D13×C47 #49144047

order36660
automorphism?
homologyAbelianization (H1) = C22×C3×C47 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×D13×C47

Splittings

Fitting, socle, HallC3×C5×C13×C47 ⋊ C22
derived, HallC5×C13 ⋊ C22×C3×C47
HallC5×C13×C47 ⋊ C22×C3
HallC3×C13×C47 ⋊ C2×D5
HallC3×C5×C47 ⋊ C2×D13
HallC13×C47 ⋊ C2×C3×D5
HallC5×C47 ⋊ C2×C3×D13
HallC3×C5×C13 ⋊ C22×C47
HallC3×C13 ⋊ C2×D5×C47
HallC3×C5 ⋊ C2×D13×C47
SylowC13 ⋊ C2×C3×D5×C47
SylowC5 ⋊ C2×C3×D13×C47

Subgroups

subgroupG/H
center, hypercenterC3×C47D5×D13
commutator, cosocle, hypocenterC5×C13C22×C3×C47
FrattiniC1G
Fitting, socleC3×C5×C13×C47C22
LCSG ▷ C5×C13
UCSC1 ◁ C3×C47

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9165

Conjugacy classes & character table

4512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36660, 67);