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D19⋊C3×C29⋊C7 #37529050

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

Aliases

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

Splittings

Fitting, socle, derived, HallC19×C29 ⋊ C2×C3×C7
HallC19⋊C3×C29⋊C7 ⋊ C2
HallD19×C29⋊C7 ⋊ C3
HallC19×C29⋊C7 ⋊ C2×C3
HallC29×D19⋊C3 ⋊ C7
HallC29×C19⋊C3 ⋊ C2×C7
HallC29×D19 ⋊ C3×C7
HallC19⋊C3 ⋊ C2×C29⋊C7
HallD19 ⋊ C3×C29⋊C7
SylowC29 ⋊ C7×D19⋊C3
SylowC19 ⋊ C2×C3×C29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC19×C29C2×C3×C7
LCSG ▷ C19×C29
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 551

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23142, 59);