Finite Group Databasebeta

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C2×C3×C5×C31×D17 #44539398

order31620
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C31 · Schur multiplier (H2) = C2

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C31D17
commutator, cosocle, hypocenterC17C22×C3×C5×C31
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C31C2
LCSG ▷ C17
UCSC1 ◁ C2×C3×C5×C31

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15810

Conjugacy classes & character table

9300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 155);