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C4×C11⋊C5×ΓL(1,𝔽32) #46801995

order34100
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC4×C11⋊C5×ΓL(1,𝔽32)
unambiguous semidirect product(C4×C11×ΓL(1,𝔽32))⋊C5
unambiguous semidirect product(C4×C31×C11⋊C5)⋊C5
unambiguous semidirect product(C4×#13133721)⋊C5
unambiguous semidirect product(C4×#13133723)⋊C5
unambiguous semidirect product(C4×#13133722)⋊C5
unambiguous semidirect product(C4×#13133724)⋊C5

Splittings

Fitting, HallC4×C11×C31 ⋊ C52
derived, HallC11×C31 ⋊ C4×C52
HallC4×C31 ⋊ C5×C11⋊C5
HallC4×C11 ⋊ C5×ΓL(1,𝔽32)
SylowC31 ⋊ C4×C5×C11⋊C5
SylowC11 ⋊ C4×C5×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC4C11⋊C5×ΓL(1,𝔽32)
commutator, hypocenterC11×C31C4×C52
FrattiniC2C2×C11⋊C5×ΓL(1,𝔽32)
FittingC4×C11×C31C52
socle, cosocleC2×C11×C31C2×C52
prime radicalC2×C11⋊C5×ΓL(1,𝔽32)C2
LCSG ▷ C11×C31
UCSC1 ◁ C4

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1364

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 86);