Finite Group Databasebeta

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C2×C31×D285 #47977779

order35340
automorphism?
homologyAbelianization (H1) = C22×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C31×D285
unambiguous semidirect product(C2×C3)⋊(C31×D95)
unambiguous semidirect product(C2×C5)⋊(C31×D57)
unambiguous semidirect product(C2×C19)⋊(D15×C31)

Splittings

Fitting, socleC2×C3×C5×C19×C31 ⋊ C2
derived, HallC3×C5×C19 ⋊ C22×C31
HallC3×C5×C19×C31 ⋊ C22
HallC5×C19×C31 ⋊ C2×D3
HallC3×C19×C31 ⋊ C2×D5
HallC19×C31 ⋊ C2×D15
HallC3×C5×C31 ⋊ C2×D19
HallC5×C31 ⋊ C2×D57
HallC5×C19 ⋊ C2×D3×C31
HallC3×C31 ⋊ C2×D95
HallC3×C19 ⋊ C2×D5×C31
SylowC19 ⋊ C2×D15×C31
HallC3×C5 ⋊ C2×C31×D19
SylowC5 ⋊ C2×C31×D57
SylowC3 ⋊ C2×C31×D95

Subgroups

subgroupG/H
center, hypercenterC2×C31D285
commutator, cosocle, hypocenterC3×C5×C19C22×C31
FrattiniC1G
Fitting, socleC2×C3×C5×C19×C31C2
LCSG ▷ C3×C5×C19
UCSC1 ◁ C2×C31

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17670

Conjugacy classes & character table

8928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 251);