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C2×C11×#10587723 #26046509

order12012
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×#10587723

Splittings

Fitting, socleC2×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C22×C3×C11
HallC2×C11×D91 ⋊ C3
HallC11×#63271 ⋊ C22
HallC7×C11×C13 ⋊ C22×C3
HallC2×D91 ⋊ C3×C11
Hall#63271 ⋊ C22×C11
HallC11×C13 ⋊ C2×AGL(1,𝔽7)
HallC7×C11 ⋊ C2×D13⋊C3
SylowC13 ⋊ C2×C11×AGL(1,𝔽7)
SylowC7 ⋊ C2×C11×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11#10587723
commutator, cosocle, hypocenterC7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

462 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11×ΓL(1,𝔽8)⋊(D13⋊C3), D3×C11×#10587723, C2×C3×C11×#10587723, …
maximal normal subgroup ofC2×C11×ΓL(1,𝔽8)⋊(D13⋊C3), C2×C3×C11×#10587723
maximal quotient ofC2×C11×#13109903, D3×C11×#10587723, C2×C3×C11×#10587723, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 99);