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Cayley diagram

C5×D44 #89173

order440
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D44
unambiguous semidirect productC4⋊(C5×D11)

Splittings

FittingC4×C5×C11 ⋊ C2
HallC5×C11 ⋊ D4
SylowC11 ⋊ C5×D4

Subgroups

subgroupG/H
centerC2×C5C2×D11
commutator, cosocleC2×C11C22×C5
FrattiniC2C2×C5×D11
FittingC4×C5×C11C2
socleC2×C5×C11C22
hypercenterC4×C5D11
hypocenterC11C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C5 ◁ C4×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 20 points:

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

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11724871, #11724872, #11724874, …
maximal normal subgroup of#11724871, #11724872, #11724874, …
maximal quotient ofC5×#4314, C5×D88, C5×Dic44, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 26);