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C2×C3×D17×ΓL(1,𝔽32) #44539322

order31620
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D17×ΓL(1,𝔽32)
unambiguous semidirect productC17⋊(C22×C3×ΓL(1,𝔽32))
unambiguous semidirect product(C2×C17)⋊(C2×C3×ΓL(1,𝔽32))
unambiguous semidirect product(C2×C3×C31×D17)⋊C5

Splittings

Fitting, socleC2×C3×C17×C31 ⋊ C2×C5
derived, HallC17×C31 ⋊ C22×C3×C5
HallC3×C17×ΓL(1,𝔽32) ⋊ C22
HallC2×C3×C31×D17 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C22×C3
HallC2×C31×D17 ⋊ C3×C5
HallC3×C17×C31 ⋊ C22×C5
HallC3×C31 ⋊ C2×C5×D17
HallC3×C17 ⋊ C22×ΓL(1,𝔽32)
SylowC31 ⋊ C2×C3×C5×D17
SylowC17 ⋊ C22×C3×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C3D17×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC17×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C17×C31C2×C5
LCSG ▷ C17×C31
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3162

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 79);