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C13×(C5⋊D5)⋊(C19⋊C3) #49150245

order37050
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C5

Aliases

direct productC13×(C5⋊D5)⋊(C19⋊C3)
unambiguous semidirect product(C5⋊D5)⋊(C13×C19⋊C3)

Splittings

Fitting, socle, HallC52×C13×C19 ⋊ C2×C3
derived, HallC52×C19 ⋊ C2×C3×C13
HallC13×C19⋊(C52⋊C3) ⋊ C2
HallC13×C19×C5⋊D5 ⋊ C3
HallC19⋊(C52⋊C3) ⋊ C2×C13
HallC19×C5⋊D5 ⋊ C3×C13
HallC13×C5⋊D5 ⋊ C19⋊C3
HallC52×C13 ⋊ C2×C19⋊C3
HallC13×C19 ⋊ (C5⋊D5)⋊C3
HallC5⋊D5 ⋊ C13×C19⋊C3
SylowC52 ⋊ C2×C13×C19⋊C3
SylowC19 ⋊ C13×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC13(C5⋊D5)⋊(C19⋊C3)
commutator, cosocle, hypocenterC52×C19C2×C3×C13
FrattiniC1G
Fitting, socleC52×C13×C19C2×C3
LCSG ▷ C52×C19
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3705

Conjugacy classes & character table

1222 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 71);