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Cayley diagram

D9×3−1+2 #92256

order486
isoclinismisoclinic class of D9×H(3,𝔽3)
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C1

Aliases

direct productD9×3−1+2

Splittings

Fitting, SylowC9×3−1+2 ⋊ C2

Subgroups

subgroupG/H
centerC3C32×D9
commutator, cosocleC3×C9C2×C32
Frattini, socleC32C32×D3
FittingC9×3−1+2C2
prime radicalC32×D9C3
hypercenter3−1+2D9
hypocenterC9C2×3−1+2
LCSG ▷ C3×C9 ▷ C9
UCSC1 ◁ C3 ◁ 3−1+2

73 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 54

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

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×AGL(1,ℤ/9), C2×D9×3−1+2, D9×AΣL(1,𝔽27), …
maximal normal subgroup ofD9×AGL(1,ℤ/9), C2×D9×3−1+2, D9×AΣL(1,𝔽27), …
maximal quotient of3−1+2×Dic9, C2×D9×3−1+2, D9×C32⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 101);