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C17×C22⋊((C31⋊C3)⋊C5) #44539298

order31620
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×C22⋊((C31⋊C3)⋊C5)
unambiguous semidirect productC22⋊(C17×(C31⋊C3)⋊C5)
unambiguous semidirect product(C22×C17)⋊((C31⋊C3)⋊C5)
unambiguous semidirect productΓL(1,𝔽32)⋊(A4×C17)
unambiguous semidirect product(C22⋊(C31⋊C3))⋊(C5×C17)
unambiguous semidirect product(C17×ΓL(1,𝔽32))⋊A4
unambiguous semidirect product(C17×C22⋊(C31⋊C3))⋊C5

Splittings

Fitting, socle, HallC22×C17×C31 ⋊ C3×C5
derived, HallC22×C31 ⋊ C3×C5×C17
HallC22×C17×ΓL(1,𝔽32) ⋊ C3
HallC17×C22⋊(C31⋊C3) ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ A4
HallC22×ΓL(1,𝔽32) ⋊ C3×C17
HallC17×C31 ⋊ C5×A4
HallC22⋊(C31⋊C3) ⋊ C5×C17
HallΓL(1,𝔽32) ⋊ A4×C17
HallC22×C17 ⋊ (C31⋊C3)⋊C5
SylowC31 ⋊ C5×A4×C17
SylowC22 ⋊ C17×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC17C22⋊((C31⋊C3)⋊C5)
commutator, cosocle, hypocenterC22×C31C3×C5×C17
FrattiniC1G
Fitting, socleC22×C17×C31C3×C5
LCSG ▷ C22×C31
UCSC1 ◁ C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2108

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 55);