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C32×C13×D31⋊C5 #49136597

order36270
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C13 · Schur multiplier (H2) = C3

Aliases

direct productC32×C13×D31⋊C5
unambiguous semidirect product(C32×D31)⋊(C5×C13)
unambiguous semidirect product(C32×C13×D31)⋊C5

Splittings

Fitting, socle, HallC32×C13×C31 ⋊ C2×C5
derived, SylowC31 ⋊ C2×C32×C5×C13
HallC32×C13×ΓL(1,𝔽32) ⋊ C2
HallC32×C13×D31 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C32
HallC32×ΓL(1,𝔽32) ⋊ C2×C13
HallC13×D31 ⋊ C32×C5
HallC32×D31 ⋊ C5×C13
HallC13×C31 ⋊ C2×C32×C5
HallC32×C31 ⋊ C2×C5×C13
HallΓL(1,𝔽32) ⋊ C2×C32×C13
HallD31 ⋊ C32×C5×C13

Subgroups

subgroupG/H
center, hypercenterC32×C13D31⋊C5
commutator, cosocle, hypocenterC31C2×C32×C5×C13
FrattiniC1G
Fitting, socleC32×C13×C31C2×C5
LCSG ▷ C31
UCSC1 ◁ C32×C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3627

Conjugacy classes & character table

1521 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 117);