Finite Group Databasebeta

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C2×C31×D255 #44539410

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

Aliases

direct productC2×C31×D255
unambiguous semidirect product(C2×C3)⋊(C31×D85)
unambiguous semidirect product(C2×C5)⋊(C31×D51)
unambiguous semidirect product(C2×C17)⋊(D15×C31)

Splittings

Fitting, socleC2×C3×C5×C17×C31 ⋊ C2
derived, HallC3×C5×C17 ⋊ C22×C31
HallC3×C5×C17×C31 ⋊ C22
HallC5×C17×C31 ⋊ C2×D3
HallC3×C17×C31 ⋊ C2×D5
HallC17×C31 ⋊ C2×D15
HallC3×C5×C31 ⋊ C2×D17
HallC5×C31 ⋊ C2×D51
HallC3×C31 ⋊ C2×D85
HallC5×C17 ⋊ C2×D3×C31
HallC3×C17 ⋊ C2×D5×C31
SylowC17 ⋊ C2×D15×C31
HallC3×C5 ⋊ C2×C31×D17
SylowC5 ⋊ C2×C31×D51
SylowC3 ⋊ C2×C31×D85

Subgroups

subgroupG/H
center, hypercenterC2×C31D255
commutator, cosocle, hypocenterC3×C5×C17C22×C31
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C31C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C2×C31

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15810

Conjugacy classes & character table

7998 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 167);