Finite Group Databasebeta

← Prev (#45654450) Next (#45654452) →

C7×D5×(C31⋊C3)⋊C5 #45654451

order32550
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D5×(C31⋊C3)⋊C5
unambiguous semidirect productC5⋊(C2×C7×(C31⋊C3)⋊C5)
unambiguous semidirect product(D5×C31⋊C3)⋊(C5×C7)
unambiguous semidirect product(D5×ΓL(1,𝔽32))⋊(C3×C7)
unambiguous semidirect product(C7×D5×C31⋊C3)⋊C5

Splittings

Fitting, socleC5×C7×C31 ⋊ C2×C3×C5
derivedC5×C31 ⋊ C2×C3×C5×C7
HallC5×C7×(C31⋊C3)⋊C5 ⋊ C2
HallC7×D5×ΓL(1,𝔽32) ⋊ C3
HallC5×C7×ΓL(1,𝔽32) ⋊ C2×C3
HallC5×(C31⋊C3)⋊C5 ⋊ C2×C7
HallD5×ΓL(1,𝔽32) ⋊ C3×C7
HallC5×ΓL(1,𝔽32) ⋊ C2×C3×C7
HallC7×C31⋊C3 ⋊ C5×D5
HallC7×C31 ⋊ C3×C5×D5
HallC31⋊C3 ⋊ C5×C7×D5
SylowC31 ⋊ C3×C5×C7×D5

Subgroups

subgroupG/H
center, hypercenterC7D5×(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC5×C31C2×C3×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C31C2×C3×C5
LCSG ▷ C5×C31
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1085

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 87);