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C4×C17×ΓL(1,𝔽32) #24902012

order10540
isoclinismisoclinic class of ΓL(1,𝔽32)
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×ΓL(1,𝔽32)
unambiguous semidirect product(C4×C31)⋊(C5×C17)
unambiguous semidirect product(C4×C17×C31)⋊C5

Splittings

Fitting, HallC4×C17×C31 ⋊ C5
derived, SylowC31 ⋊ C4×C5×C17
HallC17×C31 ⋊ C4×C5
HallC4×C31 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17ΓL(1,𝔽32)
commutator, hypocenterC31C4×C5×C17
FrattiniC2C2×C17×ΓL(1,𝔽32)
FittingC4×C17×C31C5
socleC2×C17×C31C2×C5
prime radicalC2×C17×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C5×C17
LCSG ▷ C31
UCSC1 ◁ C4×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C17×ΓL(1,𝔽32), C4×C17×(C31⋊C3)⋊C5, Dic3×C17×ΓL(1,𝔽32)
maximal normal subgroup ofC3×C4×C17×ΓL(1,𝔽32), C4×C17×(C31⋊C3)⋊C5
maximal quotient ofC3×C4×C17×ΓL(1,𝔽32), Dic3×C17×ΓL(1,𝔽32)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10540, 2);