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C3×C7×C5⋊(D31⋊C3) #34086236

order19530
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×C5⋊(D31⋊C3)
unambiguous semidirect productC5⋊(C3×C7×D31⋊C3)
unambiguous semidirect product(C31⋊C3)⋊(C3×C7×D5)
unambiguous semidirect productD155⋊(C32×C7)
unambiguous semidirect product(C3×D155)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C31 ⋊ C2×C3
derived, HallC5×C31 ⋊ C2×C32×C7
HallC3×C5×C7×C31⋊C3 ⋊ C2
HallC7×D155 ⋊ C32
HallC3×C7×C31⋊C3 ⋊ D5
HallC3×C5×C31⋊C3 ⋊ C2×C7
HallC5×C7×C31 ⋊ C2×C32
HallD155 ⋊ C32×C7
HallC3×C31⋊C3 ⋊ C7×D5
HallC7×C31 ⋊ C32×D5
HallC5×C7 ⋊ C3×D31⋊C3
SylowC31 ⋊ C32×C7×D5
SylowC5 ⋊ C3×C7×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C7C5⋊(D31⋊C3)
commutator, cosocle, hypocenterC5×C31C2×C32×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C3×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3255

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 141);