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C3⋊(#13094090⋊C7) #44539790

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

Aliases

unambiguous semidirect productC3⋊(#13094090⋊C7)
unambiguous semidirect product(C3⋊#13094090)⋊C7

Splittings

Fitting, socle, derived, HallC3×C13×C29 ⋊ C4×C7
HallC3×C13×C29⋊C7 ⋊ C4
HallC3⋊#13094090 ⋊ C7
HallC13×C29⋊C7 ⋊ Dic3
HallC3×C29⋊C7 ⋊ Dic13
HallC13×C29 ⋊ C7×Dic3
HallC29⋊C7 ⋊ Dic39
HallC3×C29 ⋊ C7×Dic13
HallC3×C13 ⋊ AGL(1,𝔽29)
SylowC29 ⋊ C7×Dic39
SylowC13 ⋊ C3⋊AGL(1,𝔽29)
SylowC3 ⋊ #13094090⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C13×C29C4×C7
prime radicalC3×C13×D29⋊C7C2
cosocleC3×C13×D29C2×C7
LCSG ▷ C3×C13×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1131

Polycyclic presentation:

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

Conjugacy classes & character table

333 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 85);