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C29×#11763961 #44539749

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

Aliases

direct productC29×#11763961

Splittings

derived, HallC7×C13 ⋊ C3×C4×C29
HallC13×Dic7×C29 ⋊ C3
HallC29×#63270 ⋊ C4
HallC7×C13×C29 ⋊ C3×C4
HallDic7×C29 ⋊ C13⋊C3
HallC13×C29 ⋊ ΓL(1,𝔽8)⋊C4
HallC13×Dic7 ⋊ C3×C29
Hall#63270 ⋊ C4×C29
HallC7×C29 ⋊ C4×C13⋊C3
HallDic7 ⋊ C29×C13⋊C3
SylowC13 ⋊ C29×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C4×C29×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C29#10587720
commutator, hypocenterC7×C13C3×C4×C29
FrattiniC2C29×#10587720
Fitting, socleC2×C7×C13×C29C2×C3
prime radicalC2×C29×#63270C2
cosocleC2×C7×C13C2×C3×C29
LCSG ▷ C7×C13
UCSC1 ◁ C2×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10556

Conjugacy classes & character table

1566 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 44);