Finite Group Databasebeta

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C2×C17×C3⋊(D31⋊C5) #44539323

order31620
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×C3⋊(D31⋊C5)
unambiguous semidirect product(C2×C3)⋊(C17×D31⋊C5)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(D3×C17)
unambiguous semidirect product(C2×D93)⋊(C5×C17)
unambiguous semidirect product(C2×C17×D93)⋊C5

Splittings

Fitting, socleC2×C3×C17×C31 ⋊ C2×C5
derived, HallC3×C31 ⋊ C22×C5×C17
HallC3×C17×ΓL(1,𝔽32) ⋊ C22
HallC2×C17×D93 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C2×D3
HallC3×C17×C31 ⋊ C22×C5
HallC17×C31 ⋊ C2×C5×D3
HallC3×ΓL(1,𝔽32) ⋊ C22×C17
HallC2×D93 ⋊ C5×C17
HallΓL(1,𝔽32) ⋊ C2×D3×C17
HallC3×C17 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C5×D3×C17
SylowC3 ⋊ C2×C17×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊(D31⋊C5)
commutator, cosocle, hypocenterC3×C31C22×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C17×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C2×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3162

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 80);