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D31×C5⋊(D19⋊C3) #47977657

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

Aliases

direct productD31×C5⋊(D19⋊C3)
unambiguous semidirect product(C19⋊C3×D31)⋊D5

Splittings

Fitting, socle, derived, HallC5×C19×C31 ⋊ C22×C3
HallD31×D95 ⋊ C3
HallC5×C31×C19⋊C3 ⋊ C22
HallC31×C19⋊C3 ⋊ C2×D5
HallC19×C31 ⋊ C2×C3×D5
HallC5×C19⋊C3 ⋊ C2×D31
HallC5×C31 ⋊ C2×D19⋊C3
HallC5×C19 ⋊ C2×C3×D31
HallC19⋊C3 ⋊ D5×D31
SylowC31 ⋊ C2×C5⋊(D19⋊C3)
SylowC19 ⋊ C3×D5×D31
SylowC5 ⋊ D31×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C19×C31C22×C3
LCSG ▷ C5×C19×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2945

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 129);