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C29×#11763979 #44539870

order31668
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×#11763979

Splittings

Fitting, socle, HallC7×C13×C29 ⋊ C3×C4
derived, HallC7×C13 ⋊ C3×C4×C29
HallC29×C7⋊#261 ⋊ C3
HallC7×C29×C13⋊C3 ⋊ C4
HallC29×C13⋊C3 ⋊ Dic7
HallC13×C29 ⋊ C3×Dic7
HallC7⋊#261 ⋊ C3×C29
HallC7×C13⋊C3 ⋊ C4×C29
HallC7×C29 ⋊ AGL(1,𝔽13)
HallC13⋊C3 ⋊ Dic7×C29
SylowC13 ⋊ C3×Dic7×C29
SylowC7 ⋊ C29×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC29#11763979
commutator, hypocenterC7×C13C3×C4×C29
FrattiniC1G
Fitting, socleC7×C13×C29C3×C4
prime radicalC7×C29×D13⋊C3C2
cosocleC7×D13C2×C3×C29
LCSG ▷ C7×C13
UCSC1 ◁ C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2639

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 165);