Finite Group Databasebeta

← Prev (#32915550) Next (#32915552) →

C2×D17×#63270 #32915551

order18564
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×D17×#63270
unambiguous semidirect productC17⋊(C22×#63270)
unambiguous semidirect product(C2×C17)⋊(C2×#63270)

Splittings

Fitting, socleC2×C7×C13×C17 ⋊ C2×C3
derived, HallC7×C13×C17 ⋊ C22×C3
HallC2×C7×C13×D17 ⋊ C3
HallC17×#63270 ⋊ C22
HallC2×C13×D17 ⋊ ΓL(1,𝔽8)
HallC2×C7×D17 ⋊ C13⋊C3
HallC13×C17 ⋊ C22×ΓL(1,𝔽8)
HallC7×C17 ⋊ C22×C13⋊C3
HallC7×C13 ⋊ C2×C3×D17
SylowC17 ⋊ C22×#63270
SylowC13 ⋊ C2×ΓL(1,𝔽8)×D17
SylowC7 ⋊ C2×D17×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2D17×#63270
commutator, cosocle, hypocenterC7×C13×C17C22×C3
FrattiniC1G
Fitting, socleC2×C7×C13×C17C2×C3
LCSG ▷ C7×C13×C17
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3094

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 146);