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C7×C23⋊(D19⋊C3) #32913474

order18354
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23⋊(D19⋊C3)
unambiguous semidirect productC23⋊(C7×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C7×D23)
unambiguous semidirect productD437⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C19×C23 ⋊ C2×C3
derived, HallC19×C23 ⋊ C2×C3×C7
HallC7×C23×C19⋊C3 ⋊ C2
HallC7×D437 ⋊ C3
HallC23×C19⋊C3 ⋊ C2×C7
HallD437 ⋊ C3×C7
HallC7×C19⋊C3 ⋊ D23
HallC7×C23 ⋊ D19⋊C3
HallC7×C19 ⋊ C3×D23
HallC19⋊C3 ⋊ C7×D23
SylowC23 ⋊ C7×D19⋊C3
SylowC19 ⋊ C3×C7×D23

Subgroups

subgroupG/H
center, hypercenterC7C23⋊(D19⋊C3)
commutator, cosocle, hypocenterC19×C23C2×C3×C7
FrattiniC1G
Fitting, socleC7×C19×C23C2×C3
LCSG ▷ C19×C23
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3059

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×D23×D19⋊C3, D7×C23⋊(D19⋊C3), ((C19⋊C3)⋊D7)⋊D23, …
maximal normal subgroup ofC7×D23×D19⋊C3, D7×C23⋊(D19⋊C3), ((C19⋊C3)⋊D7)⋊D23, …
maximal quotient ofC7×C23⋊((C19⋊C3)⋊C4), C2×C7×C23⋊(D19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18354, 29);