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C52×(C19⋊C3)⋊D13 #49150273

order37050
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×(C19⋊C3)⋊D13
unambiguous semidirect product(C19⋊C3)⋊(C52×D13)

Splittings

Fitting, socle, HallC52×C13×C19 ⋊ C2×C3
derived, HallC13×C19 ⋊ C2×C3×C52
HallC52×C13×C19⋊C3 ⋊ C2
HallC52×D247 ⋊ C3
HallC52×C19⋊C3 ⋊ D13
HallC13×C19⋊C3 ⋊ C2×C52
HallD247 ⋊ C3×C52
HallC52×C19 ⋊ C3×D13
HallC52×C13 ⋊ D19⋊C3
HallC19⋊C3 ⋊ C52×D13
SylowC19 ⋊ C3×C52×D13
SylowC13 ⋊ C52×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC52(C19⋊C3)⋊D13
commutator, cosocle, hypocenterC13×C19C2×C3×C52
FrattiniC1G
Fitting, socleC52×C13×C19C2×C3
LCSG ▷ C13×C19
UCSC1 ◁ C52

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6175

Conjugacy classes & character table

1575 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 99);