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C3×((C31⋊C3)⋊C5)⋊D7 #34086183

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

Aliases

direct productC3×((C31⋊C3)⋊C5)⋊D7
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C3×D7)
unambiguous semidirect product(C3×(C31⋊C3)⋊D7)⋊C5

Splittings

Fitting, socleC3×C7×C31 ⋊ C2×C3×C5
derived, HallC7×C31 ⋊ C2×C32×C5
HallC3×C7×(C31⋊C3)⋊C5 ⋊ C2
HallC3×(C31⋊C3)⋊D7 ⋊ C5
HallC7⋊(D31⋊C5) ⋊ C32
HallC3×C7×C31⋊C3 ⋊ C2×C5
HallC3×(C31⋊C3)⋊C5 ⋊ D7
HallC7×ΓL(1,𝔽32) ⋊ C2×C32
HallD217 ⋊ C32×C5
HallC3×C31⋊C3 ⋊ C5×D7
HallΓL(1,𝔽32) ⋊ C32×D7
SylowC31 ⋊ C32×C5×D7
SylowC7 ⋊ C3×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, hypercenterC3((C31⋊C3)⋊C5)⋊D7
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

246 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 88);