Finite Group Databasebeta

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C2×C9×D451 #30634083

order16236
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D451
unambiguous semidirect product(C2×C11)⋊(C9×D41)
unambiguous semidirect product(C2×C41)⋊(C9×D11)

Splittings

FittingC2×C9×C11×C41 ⋊ C2
derived, HallC11×C41 ⋊ C22×C9
HallC9×C11×C41 ⋊ C22
HallC9×C41 ⋊ C2×D11
HallC9×C11 ⋊ C2×D41
SylowC41 ⋊ C2×C9×D11
SylowC11 ⋊ C2×C9×D41

Subgroups

subgroupG/H
center, hypercenterC2×C9D451
commutator, hypocenterC11×C41C22×C9
FrattiniC3C2×C3×D451
FittingC2×C9×C11×C41C2
socleC2×C3×C11×C41C2×C3
prime radicalC2×C3×D451C3
cosocleC3×C11×C41C22×C3
LCSG ▷ C11×C41
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8118

Conjugacy classes & character table

4086 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16236, 26);