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C13×ΓL(1,𝔽8)×Dic29 #44539736

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

Aliases

direct productC13×ΓL(1,𝔽8)×Dic29
unambiguous semidirect product(C7×Dic29)⋊(C3×C13)

Splittings

derived, HallC7×C29 ⋊ C3×C4×C13
HallC7×C13×Dic29 ⋊ C3
HallC13×ΓL(1,𝔽8)×C29 ⋊ C4
HallC7×C13×C29 ⋊ C3×C4
HallC7×Dic29 ⋊ C3×C13
HallΓL(1,𝔽8)×C29 ⋊ C4×C13
HallC13×C29 ⋊ C4×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×Dic29
SylowC29 ⋊ C4×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C13×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C13ΓL(1,𝔽8)×D29
commutator, hypocenterC7×C29C3×C4×C13
FrattiniC2C13×ΓL(1,𝔽8)×D29
Fitting, socleC2×C7×C13×C29C2×C3
prime radicalC2×C13×ΓL(1,𝔽8)×C29C2
cosocleC2×C7×C29C2×C3×C13
LCSG ▷ C7×C29
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10556

Conjugacy classes & character table

2080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 31);