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C29×ΓL(1,𝔽8)⋊#261 #44539835

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

Aliases

direct productC29×ΓL(1,𝔽8)⋊#261
unambiguous semidirect productΓL(1,𝔽8)⋊(C29×#261)

Splittings

Fitting, socle, HallC7×C13×C29 ⋊ C3×C4
derived, HallC7×C13 ⋊ C3×C4×C29
HallC29×C7⋊#261 ⋊ C3
HallC13×ΓL(1,𝔽8)×C29 ⋊ C4
HallΓL(1,𝔽8)×C29 ⋊ #261
HallC13×C29 ⋊ ΓL(1,𝔽8)⋊C4
HallC7⋊#261 ⋊ C3×C29
HallC13×ΓL(1,𝔽8) ⋊ C4×C29
HallC7×C29 ⋊ C3×#261
HallΓL(1,𝔽8) ⋊ C29×#261
SylowC13 ⋊ C29×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C29×#261

Subgroups

subgroupG/H
center, hypercenterC29ΓL(1,𝔽8)⋊#261
commutator, hypocenterC7×C13C3×C4×C29
FrattiniC1G
Fitting, socleC7×C13×C29C3×C4
prime radicalΓL(1,𝔽8)×D13×C29C2
cosocleC7×D13C2×C3×C29
LCSG ▷ C7×C13
UCSC1 ◁ C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2639

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 130);