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C13×ΓL(1,𝔽8)⋊#1181 #44539813

order31668
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)⋊#1181
unambiguous semidirect productΓL(1,𝔽8)⋊(C13×#1181)
unambiguous semidirect product(C7⋊#1181)⋊(C3×C13)

Splittings

Fitting, socle, HallC7×C13×C29 ⋊ C3×C4
derived, HallC7×C29 ⋊ C3×C4×C13
HallC13×C7⋊#1181 ⋊ C3
HallC13×ΓL(1,𝔽8)×C29 ⋊ C4
HallC7⋊#1181 ⋊ C3×C13
HallΓL(1,𝔽8)×C29 ⋊ C4×C13
HallC13×C29 ⋊ ΓL(1,𝔽8)⋊C4
HallC13×ΓL(1,𝔽8) ⋊ #1181
HallC7×C13 ⋊ C3×#1181
SylowC29 ⋊ C13×ΓL(1,𝔽8)⋊C4
HallΓL(1,𝔽8) ⋊ C13×#1181
SylowC7 ⋊ C3×C13×#1181

Subgroups

subgroupG/H
center, hypercenterC13ΓL(1,𝔽8)⋊#1181
commutator, hypocenterC7×C29C3×C4×C13
FrattiniC1G
Fitting, socleC7×C13×C29C3×C4
prime radicalC13×ΓL(1,𝔽8)×D29C2
cosocleC7×D29C2×C3×C13
LCSG ▷ C7×C29
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2639

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 108);