Finite Group Databasebeta

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Cayley diagram

C8×D11 #4312

order176
isoclinismisoclinic class of D11
automorphismAut(G) = C23×AGL(1,𝔽11) (order 880) · Inn(G) = D11 · Out(G) = C23×C5
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

direct productC8×D11

Splittings

FittingC8×C11 ⋊ C2
derived, SylowC11 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC8D11
commutator, hypocenterC11C2×C8
FrattiniC4C2×D11
FittingC8×C11C2
socleC2×C11C2×C4
prime radicalC2×D11C4
cosocleC4×C11C22
LCSG ▷ C11
UCSC1 ◁ C8

22 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 88

A minimal faithful permutation representation — 2 generators on 19 points:

(2,3)(4,5)(6,7)(8,9)(10,11);(1,2,4,6,8,10,11,9,7,5,3)(12,13,14,16,15,17,18,19)

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC16×D11, #66862, C2×C8×D11, …
maximal normal subgroup ofC16×D11, #66862, C2×C8×D11, …
maximal quotient ofC16×D11, #66862, C8×Dic11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 3);