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C4×C29×#63270 #44539710

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

Aliases

direct productC4×C29×#63270

Splittings

Fitting, HallC4×C7×C13×C29 ⋊ C3
derived, HallC7×C13 ⋊ C3×C4×C29
HallC7×C13×C29 ⋊ C3×C4
HallC4×C13×C29 ⋊ ΓL(1,𝔽8)
HallC4×C7×C29 ⋊ C13⋊C3
HallC13×C29 ⋊ C4×ΓL(1,𝔽8)
HallC4×C7×C13 ⋊ C3×C29
HallC7×C29 ⋊ C4×C13⋊C3
HallC4×C13 ⋊ ΓL(1,𝔽8)×C29
HallC4×C7 ⋊ C29×C13⋊C3
SylowC13 ⋊ C4×ΓL(1,𝔽8)×C29
SylowC7 ⋊ C4×C29×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C29#63270
commutator, hypocenterC7×C13C3×C4×C29
FrattiniC2C2×C29×#63270
FittingC4×C7×C13×C29C3
socleC2×C7×C13×C29C2×C3
prime radicalC2×C29×#63270C2
cosocleC2×C7×C13C2×C3×C29
LCSG ▷ C7×C13
UCSC1 ◁ C4×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10556

Conjugacy classes & character table

3828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 5);