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C17×ΓL(1,𝔽8)×D29 #35208494

order20706
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)×D29
unambiguous semidirect productC29⋊(C2×C17×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D29)⋊(C3×C17)
unambiguous semidirect product(C7×C17×D29)⋊C3

Splittings

Fitting, socle, HallC7×C17×C29 ⋊ C2×C3
derived, HallC7×C29 ⋊ C2×C3×C17
HallC17×ΓL(1,𝔽8)×C29 ⋊ C2
HallC7×C17×D29 ⋊ C3
HallΓL(1,𝔽8)×C29 ⋊ C2×C17
HallC17×C29 ⋊ C2×ΓL(1,𝔽8)
HallC7×D29 ⋊ C3×C17
HallC7×C17 ⋊ C3×D29
SylowC29 ⋊ C2×C17×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C17×D29

Subgroups

subgroupG/H
center, hypercenterC17ΓL(1,𝔽8)×D29
commutator, cosocle, hypocenterC7×C29C2×C3×C17
FrattiniC1G
Fitting, socleC7×C17×C29C2×C3
LCSG ▷ C7×C29
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3451

Conjugacy classes & character table

1360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20706, 26);