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C32×D11×ΓL(1,𝔽32) #44501796

order30690
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×D11×ΓL(1,𝔽32)

Splittings

Fitting, socle, HallC32×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C2×C32×C5
HallC32×C11×ΓL(1,𝔽32) ⋊ C2
HallC32×D11×C31 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C32
HallD11×C31 ⋊ C32×C5
HallC32×C31 ⋊ C5×D11
HallC32×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C32×C5×D11
SylowC11 ⋊ C2×C32×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC32D11×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C11×C31
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 163);