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C29×(C19⋊C3)⋊D7 #37529041

order23142
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×(C19⋊C3)⋊D7
unambiguous semidirect product(C19⋊C3)⋊(D7×C29)

Splittings

Fitting, socle, HallC7×C19×C29 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C29
HallC7×C29×C19⋊C3 ⋊ C2
HallC29×D133 ⋊ C3
HallC29×C19⋊C3 ⋊ D7
HallC19×C29 ⋊ C3×D7
HallC7×C19⋊C3 ⋊ C2×C29
HallD133 ⋊ C3×C29
HallC7×C29 ⋊ D19⋊C3
HallC19⋊C3 ⋊ D7×C29
SylowC19 ⋊ C3×D7×C29
SylowC7 ⋊ C29×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC29(C19⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C19C2×C3×C29
FrattiniC1G
Fitting, socleC7×C19×C29C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3857

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23142, 50);