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C11×#11716322⋊C2 #31798237

order17556
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×#11716322⋊C2
unambiguous semidirect product#11716322⋊(C2×C11)
unambiguous semidirect product#11716326⋊(C2×C11)
unambiguous semidirect product#11716328⋊(C2×C11)

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C22×C3
derived, HallC7×C19 ⋊ C22×C3×C11
HallC11×D7×D19 ⋊ C3
HallC11×#87705 ⋊ C22
HallD7×D19 ⋊ C3×C11
Hall#87705 ⋊ C22×C11
HallC11×C19 ⋊ C2×AGL(1,𝔽7)
HallC7×C11 ⋊ C2×D19⋊C3
SylowC19 ⋊ C2×C11×AGL(1,𝔽7)
SylowC7 ⋊ C2×C11×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC11#11716322⋊C2
commutator, cosocle, hypocenterC7×C19C22×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C19C22×C3
LCSG ▷ C7×C19
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 52);