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C3×#13049961⋊C5 #34086175

order19530
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×#13049961⋊C5
unambiguous semidirect product(C3×#13049961)⋊C5

Splittings

Fitting, socleC3×C7×C31 ⋊ C2×C3×C5
derived, HallC7×C31 ⋊ C2×C32×C5
HallC3×#10620253⋊C5 ⋊ C2
HallC3×#13049961 ⋊ C5
HallC7⋊(D31⋊C5) ⋊ C32
HallC3×#10620253 ⋊ C2×C5
HallC7×ΓL(1,𝔽32) ⋊ C2×C32
HallD217 ⋊ C32×C5
HallΓL(1,𝔽32) ⋊ C3×AGL(1,𝔽7)
SylowC31 ⋊ C3×C5×AGL(1,𝔽7)
SylowC7 ⋊ C3×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, hypercenterC3#13049961⋊C5
commutator, cosocle, hypocenterC7×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C7×C31C2×C3×C5
LCSG ▷ C7×C31
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 651

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 80);