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Cayley diagram

C22×C5×D11 #89195

order440
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC22×C5×D11

Splittings

Fitting, socleC22×C5×C11 ⋊ C2
derived, SylowC11 ⋊ C23×C5
HallC5×C11 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC22×C5D11
commutator, cosocle, hypocenterC11C23×C5
FrattiniC1G
Fitting, socleC22×C5×C11C2
LCSG ▷ C11
UCSC1 ◁ C22×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 220

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D11)⋊Dic5, C5×(C2×D11)⋊C4, C2×Dic5×D11, …
maximal normal subgroup of(C2×D11)⋊Dic5, C5×(C2×D11)⋊C4, C2×Dic5×D11, …
maximal quotient ofC2×C5×Dic22, C2×C4×C5×D11, C2×C5×D44, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 48);