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C32×D5×ΓL(1,𝔽32) #28358462

order13950
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×D5×ΓL(1,𝔽32)
unambiguous semidirect productC5⋊(C2×C32×ΓL(1,𝔽32))
unambiguous semidirect product(C32×D5×C31)⋊C5

Splittings

Fitting, socleC32×C5×C31 ⋊ C2×C5
derivedC5×C31 ⋊ C2×C32×C5
HallC32×C5×ΓL(1,𝔽32) ⋊ C2
HallC5×ΓL(1,𝔽32) ⋊ C2×C32
HallC32×C31 ⋊ C5×D5
SylowC31 ⋊ C32×C5×D5

Subgroups

subgroupG/H
center, hypercenterC32D5×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC5×C31C2×C32×C5
FrattiniC1G
Fitting, socleC32×C5×C31C2×C5
LCSG ▷ C5×C31
UCSC1 ◁ C32

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

396 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×ΓL(1,𝔽32)⋊AGL(1,𝔽5), C32×AGL(1,𝔽5)×ΓL(1,𝔽32), C32×D5×D31⋊C5, …
maximal normal subgroup ofC32×ΓL(1,𝔽32)⋊AGL(1,𝔽5), C32×AGL(1,𝔽5)×ΓL(1,𝔽32), C32×D5×D31⋊C5, …
maximal quotient ofC32×Dic5×ΓL(1,𝔽32), C2×C32×D5×ΓL(1,𝔽32)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 105);