Finite Group Databasebeta

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C2×C5×C13⋊C3×C31⋊C3 #49136608

order36270
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C5×C13⋊C3×C31⋊C3
unambiguous semidirect product(C2×C5×C13×C31⋊C3)⋊C3
unambiguous semidirect product(C2×C5×C31×C13⋊C3)⋊C3
unambiguous semidirect product(C2×C5×#11925882)⋊C3
unambiguous semidirect product(C2×C5×#11925881)⋊C3

Splittings

Fitting, socle, HallC2×C5×C13×C31 ⋊ C32
derived, HallC13×C31 ⋊ C2×C32×C5
HallC5×C13×C31 ⋊ C2×C32
HallC2×C13×C31 ⋊ C32×C5
HallC2×C5×C31 ⋊ C3×C13⋊C3
HallC5×C31 ⋊ C2×C3×C13⋊C3
HallC2×C5×C13 ⋊ C3×C31⋊C3
HallC5×C13 ⋊ C2×C3×C31⋊C3
HallC2×C31 ⋊ C3×C5×C13⋊C3
SylowC31 ⋊ C2×C3×C5×C13⋊C3
HallC2×C13 ⋊ C3×C5×C31⋊C3
SylowC13 ⋊ C2×C3×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C13⋊C3×C31⋊C3
commutator, cosocle, hypocenterC13×C31C2×C32×C5
FrattiniC1G
Fitting, socleC2×C5×C13×C31C32
LCSG ▷ C13×C31
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4030

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 128);