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C29×ΓL(1,𝔽8)⋊Dic13 #44539756

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

Aliases

direct productC29×ΓL(1,𝔽8)⋊Dic13
unambiguous semidirect productΓL(1,𝔽8)⋊(C29×Dic13)

Splittings

derived, HallC7×C13 ⋊ C3×C4×C29
HallC29×Dic91 ⋊ C3
HallC13×ΓL(1,𝔽8)×C29 ⋊ C4
HallC7×C13×C29 ⋊ C3×C4
HallΓL(1,𝔽8)×C29 ⋊ Dic13
HallC13×C29 ⋊ ΓL(1,𝔽8)⋊C4
HallDic91 ⋊ C3×C29
HallC13×ΓL(1,𝔽8) ⋊ C4×C29
HallC7×C29 ⋊ C3×Dic13
HallΓL(1,𝔽8) ⋊ C29×Dic13
SylowC13 ⋊ C29×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C29×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C29ΓL(1,𝔽8)⋊D13
commutator, hypocenterC7×C13C3×C4×C29
FrattiniC2C29×ΓL(1,𝔽8)⋊D13
Fitting, socleC2×C7×C13×C29C2×C3
prime radicalC2×C13×ΓL(1,𝔽8)×C29C2
cosocleC2×C7×C13C2×C3×C29
LCSG ▷ C7×C13
UCSC1 ◁ C2×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10556

Conjugacy classes & character table

2146 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 51);