Finite Group Databasebeta

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C2×C5⋊#16812976 #47977700

order35340
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊#16812976
unambiguous semidirect product(C2×C5)⋊#16812976

Splittings

Fitting, socleC2×C5×C19×C31 ⋊ C2×C3
derived, HallC5×C19×C31 ⋊ C22×C3
HallC2×D2945 ⋊ C3
HallC5×#13183714 ⋊ C22
Hall#13183714 ⋊ C2×D5
HallC19×C31 ⋊ C2×C3×D5
HallC5×C31 ⋊ C2×D19⋊C3
HallC5×C19 ⋊ C2×D31⋊C3
SylowC31 ⋊ C2×C5⋊(D19⋊C3)
SylowC19 ⋊ C2×C5⋊(D31⋊C3)
SylowC5 ⋊ C2×#16812976

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#16812976
commutator, cosocle, hypocenterC5×C19×C31C22×C3
FrattiniC1G
Fitting, socleC2×C5×C19×C31C2×C3
LCSG ▷ C5×C19×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5890

Conjugacy classes & character table

1004 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 172);