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C4×C13×ΓL(1,𝔽32) #22548969

order8060
isoclinismisoclinic class of ΓL(1,𝔽32)
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×ΓL(1,𝔽32)
unambiguous semidirect product(C4×C31)⋊(C5×C13)
unambiguous semidirect product(C4×C13×C31)⋊C5

Splittings

Fitting, HallC4×C13×C31 ⋊ C5
derived, SylowC31 ⋊ C4×C5×C13
HallC13×C31 ⋊ C4×C5
HallC4×C31 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC4×C13ΓL(1,𝔽32)
commutator, hypocenterC31C4×C5×C13
FrattiniC2C2×C13×ΓL(1,𝔽32)
FittingC4×C13×C31C5
socleC2×C13×C31C2×C5
LCSG ▷ C31
UCSC1 ◁ C4×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C13×ΓL(1,𝔽32), C4×C13×(C31⋊C3)⋊C5, C4×C13⋊C3×ΓL(1,𝔽32), …
maximal normal subgroup ofC3×C4×C13×ΓL(1,𝔽32), C4×C13×(C31⋊C3)⋊C5, C4×C13⋊C3×ΓL(1,𝔽32), …
maximal quotient ofC3×C4×C13×ΓL(1,𝔽32), Dic3×C13×ΓL(1,𝔽32)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8060, 2);