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C7×#13094087⋊C3 #44539807

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

Aliases

direct productC7×#13094087⋊C3

Splittings

Fitting, socle, HallC7×C13×C29 ⋊ C3×C4
derived, HallC13×C29 ⋊ C3×C4×C7
HallC7×#13094087 ⋊ C3
HallC7×C29×C13⋊C3 ⋊ C4
Hall#13094087 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C4×C7
HallC7×C13⋊C3 ⋊ #1181
HallC7×C29 ⋊ AGL(1,𝔽13)
HallC7×C13 ⋊ C3×#1181
HallC13⋊C3 ⋊ C7×#1181
SylowC29 ⋊ C7×AGL(1,𝔽13)
SylowC13 ⋊ C3×C7×#1181

Subgroups

subgroupG/H
center, hypercenterC7#13094087⋊C3
commutator, hypocenterC13×C29C3×C4×C7
FrattiniC1G
Fitting, socleC7×C13×C29C3×C4
prime radicalC7×C29⋊(D13⋊C3)C2
cosocleD377C2×C3×C7
LCSG ▷ C13×C29
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2639

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 102);