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ΓL(1,𝔽8)×C29×#261 #44539862

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

Aliases

direct productΓL(1,𝔽8)×C29×#261

Splittings

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

1015 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 157);