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C2×D11×#87704 #31798284

order17556
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×D11×#87704
unambiguous semidirect productC11⋊(C22×#87704)
unambiguous semidirect product(C2×C11)⋊(C2×#87704)

Splittings

Fitting, socleC2×C7×C11×C19 ⋊ C2×C3
derived, HallC7×C11×C19 ⋊ C22×C3
HallC2×C7×C19×D11 ⋊ C3
HallC11×#87704 ⋊ C22
HallC2×C19×D11 ⋊ ΓL(1,𝔽8)
HallC2×C7×D11 ⋊ C19⋊C3
HallC11×C19 ⋊ C22×ΓL(1,𝔽8)
HallC7×C19 ⋊ C2×C3×D11
HallC7×C11 ⋊ C22×C19⋊C3
SylowC19 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C22×#87704
SylowC7 ⋊ C2×D11×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2D11×#87704
commutator, cosocle, hypocenterC7×C11×C19C22×C3
FrattiniC1G
Fitting, socleC2×C7×C11×C19C2×C3
LCSG ▷ C7×C11×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2926

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 99);