Finite Group Databasebeta

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C3×#13094088⋊C7 #44539779

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

Aliases

direct productC3×#13094088⋊C7
unambiguous semidirect product(C3×#13094088)⋊C7

Splittings

Fitting, socle, HallC3×C13×C29 ⋊ C4×C7
derived, HallC13×C29 ⋊ C3×C4×C7
HallC3×C13×C29⋊C7 ⋊ C4
HallC3×#13094088 ⋊ C7
HallC13×C29⋊C7 ⋊ C3×C4
Hall#13094088 ⋊ C3×C7
HallC3×C29⋊C7 ⋊ #261
HallC29⋊C7 ⋊ C3×#261
HallC3×C29 ⋊ C7×#261
HallC3×C13 ⋊ AGL(1,𝔽29)
SylowC29 ⋊ C3×C7×#261
SylowC13 ⋊ C3×AGL(1,𝔽29)

Subgroups

subgroupG/H
center, hypercenterC3#13094088⋊C7
commutator, hypocenterC13×C29C3×C4×C7
FrattiniC1G
Fitting, socleC3×C13×C29C4×C7
prime radicalC3×C13⋊(D29⋊C7)C2
cosocleD377C2×C3×C7
LCSG ▷ C13×C29
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1131

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 74);