Finite Group Databasebeta

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C19⋊C3×C5⋊D65 #49150306

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

Aliases

direct productC19⋊C3×C5⋊D65
unambiguous semidirect productC5⋊(C19⋊C3×D65)

Splittings

Fitting, socle, derived, HallC52×C13×C19 ⋊ C2×C3
HallC52×C13×C19⋊C3 ⋊ C2
HallC19×C5⋊D65 ⋊ C3
HallC52×C19⋊C3 ⋊ D13
HallC13×C19⋊C3 ⋊ C5⋊D5
HallC52×C19 ⋊ C3×D13
HallC52×C13 ⋊ C2×C19⋊C3
HallC13×C19 ⋊ C3×C5⋊D5
SylowC52 ⋊ D13×C19⋊C3
SylowC19 ⋊ C3×C5⋊D65
SylowC13 ⋊ C5⋊D5×C19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C13×C19C2×C3
LCSG ▷ C52×C13×C19
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6175

Conjugacy classes & character table

1476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 132);