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ΓL(1,𝔽8)×C29×D17 #35208495

order20706
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C29×D17
unambiguous semidirect productC17⋊(C2×ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C7×D17)⋊(C3×C29)
unambiguous semidirect product(C7×C29×D17)⋊C3

Splittings

Fitting, socle, HallC7×C17×C29 ⋊ C2×C3
derived, HallC7×C17 ⋊ C2×C3×C29
HallC17×ΓL(1,𝔽8)×C29 ⋊ C2
HallC7×C29×D17 ⋊ C3
HallC17×C29 ⋊ C2×ΓL(1,𝔽8)
HallC17×ΓL(1,𝔽8) ⋊ C2×C29
HallC7×D17 ⋊ C3×C29
HallC7×C29 ⋊ C3×D17
SylowC17 ⋊ C2×ΓL(1,𝔽8)×C29
SylowC7 ⋊ C3×C29×D17

Subgroups

subgroupG/H
center, hypercenterC29ΓL(1,𝔽8)×D17
commutator, cosocle, hypocenterC7×C17C2×C3×C29
FrattiniC1G
Fitting, socleC7×C17×C29C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3451

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20706, 27);