Finite Group Databasebeta

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C7×C3⋊(C5⋊(D31⋊C3)) #34086268

order19530
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(C5⋊(D31⋊C3))
unambiguous semidirect productC3⋊(C7×C5⋊(D31⋊C3))
unambiguous semidirect productC5⋊(C7×C3⋊(D31⋊C3))
unambiguous semidirect product(C31⋊C3)⋊(C7×D15)
unambiguous semidirect productD465⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C31 ⋊ C2×C3
derivedC3×C5×C31 ⋊ C2×C3×C7
HallC3×C5×C7×C31⋊C3 ⋊ C2
HallC3×C7×C31⋊C3 ⋊ D5
HallC3×C5×C31⋊C3 ⋊ C2×C7
HallC5×C7×C31 ⋊ C3×D3
HallC3×C31⋊C3 ⋊ C7×D5
HallC7×C31 ⋊ C3×D15
HallC5×C31 ⋊ C3×D3×C7
HallC5×C7 ⋊ C3⋊(D31⋊C3)
SylowC31 ⋊ C3×C7×D15
SylowC5 ⋊ C7×C3⋊(D31⋊C3)

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C5⋊(D31⋊C3))
commutator, cosocle, hypocenterC3×C5×C31C2×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C3
LCSG ▷ C3×C5×C31
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3255

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 173);