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C29×#11763955 #44539755

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

Aliases

direct productC29×#11763955

Splittings

derived, HallC7×C13 ⋊ C3×C4×C29
HallC29×Dic91 ⋊ C3
HallC7×C29×C13⋊C3 ⋊ C4
HallC7×C13×C29 ⋊ C3×C4
HallC29×C13⋊C3 ⋊ Dic7
HallC13×C29 ⋊ C3×Dic7
HallDic91 ⋊ C3×C29
HallC7×C13⋊C3 ⋊ C4×C29
HallC7×C29 ⋊ Dic13⋊C3
HallC13⋊C3 ⋊ Dic7×C29
SylowC13 ⋊ C3×Dic7×C29
SylowC7 ⋊ C29×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C29(C13⋊C3)⋊D7
commutator, hypocenterC7×C13C3×C4×C29
FrattiniC2C29×(C13⋊C3)⋊D7
Fitting, socleC2×C7×C13×C29C2×C3
prime radicalC2×C7×C29×C13⋊C3C2
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

1682 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 50);