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C2×#16812972⋊C5 #47977609

order35340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×#16812972⋊C5
unambiguous semidirect product(C2×#16812972)⋊C5

Splittings

Fitting, socleC2×C19×C31 ⋊ C2×C3×C5
derived, HallC19×C31 ⋊ C22×C3×C5
HallC2×D19×ΓL(1,𝔽32) ⋊ C3
Hall#13183714⋊C5 ⋊ C22
HallC2×#16812972 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C22×C3
HallC2×C31×D19 ⋊ C3×C5
Hall#13183714 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C2×D19⋊C3
HallC2×D19 ⋊ (C31⋊C3)⋊C5
SylowC31 ⋊ C2×C5×D19⋊C3
SylowC19 ⋊ C22×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC2#16812972⋊C5
commutator, cosocle, hypocenterC19×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C19×C31C2×C3×C5
LCSG ▷ C19×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1178

Conjugacy classes & character table

134 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 81);