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C11×AGL(1,𝔽5)×ΓL(1,𝔽32) #46802068

order34100
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×AGL(1,𝔽5)×ΓL(1,𝔽32)
unambiguous semidirect product(AGL(1,𝔽5)×C31)⋊(C5×C11)

Splittings

Fitting, socleC5×C11×C31 ⋊ C4×C5
derivedC5×C31 ⋊ C4×C5×C11
HallC5×C11×ΓL(1,𝔽32) ⋊ C4
HallC5×ΓL(1,𝔽32) ⋊ C4×C11
HallC11×C31 ⋊ C5×AGL(1,𝔽5)
SylowC31 ⋊ C5×C11×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC11AGL(1,𝔽5)×ΓL(1,𝔽32)
commutator, hypocenterC5×C31C4×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C31C4×C5
prime radicalD5×C11×ΓL(1,𝔽32)C2
cosocleD5×C31C2×C5×C11
LCSG ▷ C5×C31
UCSC1 ◁ C11

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1705

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 159);