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Cayley diagram

D4×D11 #4340

order176
automorphismAut(G) = C2×D4×AGL(1,𝔽11) (order 1760) · Inn(G) = C22×D11 · Out(G) = C22×C5
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD4×D11

Splittings

FittingD4×C11 ⋊ C2
SylowC11 ⋊ C2×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×D11
commutator, socle, cosocleC2×C11C23
FittingD4×C11C2
hypercenterD4D11
hypocenterC11C2×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ D4

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 44

A minimal faithful permutation representation — 3 generators on 15 points:

(2,3)(4,5)(6,7)(8,9)(10,11);(1,2,4,6,8,10,11,9,7,5,3)(13,15);(12,13)(14,15)

Conjugacy classes & character table

35 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD8×D11, #66964, SD16×D11, …
maximal normal subgroup ofD8×D11, #66964, SD16×D11, …
maximal quotient of#66931, C22⋊C4×D11, (C22⋊D11)⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 31);