Finite Group Databasebeta

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C2×C5×C13×D147 #50303545

order38220
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C13×D147
unambiguous semidirect product(C2×C3)⋊(C5×C13×D49)
unambiguous semidirect product(C2×C49)⋊(C5×D3×C13)

Splittings

FittingC2×C3×C5×C13×C49 ⋊ C2
derived, HallC3×C49 ⋊ C22×C5×C13
HallC3×C5×C13×C49 ⋊ C22
HallC5×C13×C49 ⋊ C2×D3
HallC3×C13×C49 ⋊ C22×C5
HallC3×C5×C49 ⋊ C22×C13
HallC13×C49 ⋊ C2×C5×D3
HallC5×C49 ⋊ C2×D3×C13
HallC3×C5×C13 ⋊ C2×D49
SylowC49 ⋊ C2×C5×D3×C13
HallC3×C13 ⋊ C2×C5×D49
HallC3×C5 ⋊ C2×C13×D49
SylowC3 ⋊ C2×C5×C13×D49

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D147
commutator, cosocle, hypocenterC3×C49C22×C5×C13
FrattiniC7C2×C5×C13×D21
FittingC2×C3×C5×C13×C49C2
socleC2×C3×C5×C7×C13D7
LCSG ▷ C3×C49
UCSC1 ◁ C2×C5×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19110

Conjugacy classes & character table

9750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 231);