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D31⋊C3×D95 #47977673

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

Aliases

direct productD31⋊C3×D95
unambiguous semidirect productD31⋊(C3×D95)
unambiguous semidirect product(C5×D31⋊C3)⋊D19
unambiguous semidirect product(C19×D31⋊C3)⋊D5

Splittings

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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 145);