Finite Group Databasebeta

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C2×C11⋊#13049958 #43270671

order28644
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊#13049958
unambiguous semidirect product(C2×C11)⋊#13049958

Splittings

Fitting, socleC2×C7×C11×C31 ⋊ C2×C3
derived, HallC7×C11×C31 ⋊ C22×C3
HallC2×C31×D77 ⋊ C3
HallC11×#10620252 ⋊ C22
Hall#10620252 ⋊ C2×D11
HallC11×C31 ⋊ C2×AGL(1,𝔽7)
HallC2×D77 ⋊ C31⋊C3
HallC7×C31 ⋊ C2×C3×D11
HallC7×C11 ⋊ C22×C31⋊C3
SylowC31 ⋊ C2×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ C2×#13049958
SylowC7 ⋊ C2×D11×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C11⋊#13049958
commutator, cosocle, hypocenterC7×C11×C31C22×C3
FrattiniC1G
Fitting, socleC2×C7×C11×C31C2×C3
LCSG ▷ C7×C11×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4774

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28644, 90);