Finite Group Databasebeta

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C2×D11×#10625202 #45656767

order32604
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×D11×#10625202
unambiguous semidirect productC11⋊(C22×#10625202)
unambiguous semidirect product(C2×C11)⋊(C2×#10625202)

Splittings

Fitting, socleC2×C11×C13×C19 ⋊ C2×C3
derived, HallC11×C13×C19 ⋊ C22×C3
HallC2×C13×C19×D11 ⋊ C3
HallC11×#10625202 ⋊ C22
HallC2×C19×D11 ⋊ C13⋊C3
HallC2×C13×D11 ⋊ C19⋊C3
HallC13×C19 ⋊ C2×C3×D11
HallC11×C19 ⋊ C22×C13⋊C3
HallC11×C13 ⋊ C22×C19⋊C3
SylowC19 ⋊ C2×D11×C13⋊C3
SylowC13 ⋊ C2×D11×C19⋊C3
SylowC11 ⋊ C22×#10625202

Subgroups

subgroupG/H
center, hypercenterC2D11×#10625202
commutator, cosocle, hypocenterC11×C13×C19C22×C3
FrattiniC1G
Fitting, socleC2×C11×C13×C19C2×C3
LCSG ▷ C11×C13×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5434

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 117);