Finite Group Databasebeta

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C2×C3×C31×D85 #44539402

order31620
automorphism?
homologyAbelianization (H1) = C22×C3×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C31×D85
unambiguous semidirect product(C2×C5)⋊(C3×C31×D17)
unambiguous semidirect product(C2×C17)⋊(C3×D5×C31)

Splittings

Fitting, socleC2×C3×C5×C17×C31 ⋊ C2
derived, HallC5×C17 ⋊ C22×C3×C31
HallC3×C5×C17×C31 ⋊ C22
HallC5×C17×C31 ⋊ C22×C3
HallC3×C17×C31 ⋊ C2×D5
HallC17×C31 ⋊ C2×C3×D5
HallC3×C5×C31 ⋊ C2×D17
HallC3×C5×C17 ⋊ C22×C31
HallC5×C31 ⋊ C2×C3×D17
HallC3×C17 ⋊ C2×D5×C31
SylowC17 ⋊ C2×C3×D5×C31
HallC3×C5 ⋊ C2×C31×D17
SylowC5 ⋊ C2×C3×C31×D17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C31D85
commutator, cosocle, hypocenterC5×C17C22×C3×C31
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C31C2
LCSG ▷ C5×C17
UCSC1 ◁ C2×C3×C31

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15810

Conjugacy classes & character table

8184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 159);