Finite Group Databasebeta

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C5×C7×C3⋊(D31⋊C5) #45654477

order32550
automorphism?
homologyAbelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7×C3⋊(D31⋊C5)
unambiguous semidirect productC3⋊(C5×C7×D31⋊C5)
unambiguous semidirect productΓL(1,𝔽32)⋊(C5×D3×C7)
unambiguous semidirect productD93⋊(C52×C7)
unambiguous semidirect product(C5×D93)⋊(C5×C7)
unambiguous semidirect product(C7×D93)⋊C52
unambiguous semidirect product(C5×C7×D93)⋊C5

Splittings

Fitting, socleC3×C5×C7×C31 ⋊ C2×C5
derived, HallC3×C31 ⋊ C2×C52×C7
HallC3×C5×C7×ΓL(1,𝔽32) ⋊ C2
HallC5×C7×ΓL(1,𝔽32) ⋊ D3
HallC3×C5×ΓL(1,𝔽32) ⋊ C2×C7
HallC7×D93 ⋊ C52
HallC5×ΓL(1,𝔽32) ⋊ D3×C7
HallC3×C7×C31 ⋊ C2×C52
HallC7×C31 ⋊ C52×D3
HallD93 ⋊ C52×C7
SylowC31 ⋊ C52×D3×C7
HallC3×C7 ⋊ C5×D31⋊C5
SylowC3 ⋊ C5×C7×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊(D31⋊C5)
commutator, cosocle, hypocenterC3×C31C2×C52×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C5×C7

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3255

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 113);