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Cayley diagram

D5×Dic9 #67081

order360
isoclinismisoclinic class of D5×D9
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productD5×Dic9

Splittings

derived, HallC5×C9 ⋊ C2×C4
SylowC9 ⋊ C4×D5
SylowC5 ⋊ C2×Dic9

Subgroups

subgroupG/H
center, hypercenterC2D5×D9
commutator, hypocenterC5×C9C2×C4
FrattiniC2×C3D3×D5
Fitting, cosocleC2×C5×C9C22
socleC2×C3×C5C2×D3
prime radicalC2×C3×D5D3
LCSG ▷ C5×C9
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 180

A minimal faithful permutation representation — 2 generators on 18 points:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×Dic9, Dic9⋊AGL(1,𝔽5), D5×Dic18, …
maximal normal subgroup ofAGL(1,𝔽5)×Dic9, Dic9⋊AGL(1,𝔽5), D5×Dic18, …
maximal quotient ofD5×C9⋊C8, #10623547, Dic5×Dic9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 11);