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(#13094090⋊C3)⋊C7 #44539771

order31668
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(#13094090⋊C3)⋊C7
unambiguous semidirect product(#13094090⋊C7)⋊C3

Splittings

Fitting, socle, derived, HallC13×C29 ⋊ C3×C4×C7
Hall#13094090⋊C7 ⋊ C3
HallC13⋊C3×C29⋊C7 ⋊ C4
Hall#13094090⋊C3 ⋊ C7
HallC13×C29⋊C7 ⋊ C3×C4
Hall#13094090 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C4×C7
HallC29⋊C7 ⋊ Dic13⋊C3
HallC13⋊C3 ⋊ AGL(1,𝔽29)
SylowC29 ⋊ C7×Dic13⋊C3
SylowC13 ⋊ C3×AGL(1,𝔽29)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C29C3×C4×C7
prime radicalC13⋊C3×D29⋊C7C2
cosocleC13×D29C2×C3×C7
LCSG ▷ C13×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 377

Polycyclic presentation:

2,3,7,2,13,29|a^2=d,e^a=e^12,f^a=f^17,e^b=e^3,f^c=f^16,f^d=f^28

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 66);