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C2×D17×(C31⋊C3)⋊C5 #44539286

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

Aliases

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

Splittings

Fitting, socleC2×C17×C31 ⋊ C2×C3×C5
derived, HallC17×C31 ⋊ C22×C3×C5
HallC2×D17×ΓL(1,𝔽32) ⋊ C3
HallC17×(C31⋊C3)⋊C5 ⋊ C22
HallC2×D17×C31⋊C3 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C22×C3
HallC2×C31×D17 ⋊ C3×C5
HallC17×C31⋊C3 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C2×C3×D17
HallC31⋊C3 ⋊ C2×C5×D17
SylowC31 ⋊ C2×C3×C5×D17
SylowC17 ⋊ C22×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC2D17×(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC17×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C17×C31C2×C3×C5
LCSG ▷ C17×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1054

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 43);