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Cayley diagram

C11×Dic11 #92147

order484
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic11
unambiguous semidirect productC11⋊(C4×C11)

Splittings

derivedC11 ⋊ C4×C11
SylowC112 ⋊ C4

Subgroups

subgroupG/H
center, hypercenterC2×C11D11
commutator, hypocenterC11C4×C11
FrattiniC2C11×D11
Fitting, socle, prime radicalC2×C112C2
cosocleC2×C11C2×C11
LCSG ▷ C11
UCSC1 ◁ C2×C11

22 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 44

A minimal faithful permutation representation — 2 generators on 26 points:

(1,4,3,2)(5,6,7,8,9,10,11,12,13,14,15)(17,18)(19,20)(21,22)(23,24)(25,26);(16,17,19,21,23,25,26,24,22,20,18)

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×Dic11, #11757244, #11757246, …
maximal normal subgroup ofD11×Dic11, #11757244, #11757246, …
maximal quotient ofC11×C11⋊C8, C2×C11×Dic11, C3×C11×Dic11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(484, 5);