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C2×C11×C17⋊(D13⋊C3) #44415754

order29172
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C17⋊(D13⋊C3)
unambiguous semidirect product(C2×C17)⋊(C11×D13⋊C3)
unambiguous semidirect product(C2×C13⋊C3)⋊(C11×D17)
unambiguous semidirect product(C2×D221)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D221)⋊C3

Splittings

Fitting, socleC2×C11×C13×C17 ⋊ C2×C3
derived, HallC13×C17 ⋊ C22×C3×C11
HallC2×C11×D221 ⋊ C3
HallC11×C17×C13⋊C3 ⋊ C22
HallC11×C13×C17 ⋊ C22×C3
HallC2×D221 ⋊ C3×C11
HallC17×C13⋊C3 ⋊ C22×C11
HallC11×C13⋊C3 ⋊ C2×D17
HallC11×C17 ⋊ C2×D13⋊C3
HallC11×C13 ⋊ C2×C3×D17
HallC13⋊C3 ⋊ C2×C11×D17
SylowC17 ⋊ C2×C11×D13⋊C3
SylowC13 ⋊ C2×C3×C11×D17

Subgroups

subgroupG/H
center, hypercenterC2×C11C17⋊(D13⋊C3)
commutator, cosocle, hypocenterC13×C17C22×C3×C11
FrattiniC1G
Fitting, socleC2×C11×C13×C17C2×C3
LCSG ▷ C13×C17
UCSC1 ◁ C2×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4862

Conjugacy classes & character table

1408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 46);