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D11×#440 #13077391

order1408
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD11×#440

Splittings

FittingC11×#440 ⋊ C2
SylowC11 ⋊ C2×#440

Subgroups

subgroupG/H
centerC22C2×D4×D11
commutatorC4×C11C23×C4
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radicalC2×D4×D11C22
cosocleC2×C4×C11C24
hypercenter#440D11
hypocenterC11C2×#440
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D11×#440, D11×#2943, C4×D11×AGL(1,ℤ/8), …
maximal normal subgroup ofC2×D11×#440, D11×#2943, C4×D11×AGL(1,ℤ/8), …
maximal quotient ofD11×SD16⋊C8, D11×#1585, D11×#1588, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 13285);