Finite Group Databasebeta

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C7×C29×D19⋊C3 #37529025

order23142
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C29 · Schur multiplier (H2) = C1

Aliases

direct productC7×C29×D19⋊C3
unambiguous semidirect productD19⋊(C3×C7×C29)
unambiguous semidirect product(C19⋊C3)⋊(C2×C7×C29)

Splittings

Fitting, socle, HallC7×C19×C29 ⋊ C2×C3
derived, SylowC19 ⋊ C2×C3×C7×C29
HallC7×C29×C19⋊C3 ⋊ C2
HallC7×C29×D19 ⋊ C3
HallC29×C19⋊C3 ⋊ C2×C7
HallC29×D19 ⋊ C3×C7
HallC19×C29 ⋊ C2×C3×C7
HallC7×C19⋊C3 ⋊ C2×C29
HallC7×D19 ⋊ C3×C29
HallC7×C19 ⋊ C2×C3×C29
HallC19⋊C3 ⋊ C2×C7×C29
HallD19 ⋊ C3×C7×C29

Subgroups

subgroupG/H
center, hypercenterC7×C29D19⋊C3
commutator, cosocle, hypocenterC19C2×C3×C7×C29
FrattiniC1G
Fitting, socleC7×C19×C29C2×C3
LCSG ▷ C19
UCSC1 ◁ C7×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3857

Conjugacy classes & character table

1827 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23142, 34);