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Cayley diagram

C9×D27 #92168

order486
isoclinismisoclinic class of D27
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D27

Splittings

Fitting, SylowC9×C27 ⋊ C2
derivedC27 ⋊ C2×C9

Subgroups

subgroupG/H
center, hypercenterC9D27
commutator, hypocenterC27C2×C9
FrattiniC3×C9C3×D3
FittingC9×C27C2
socleC32C3×D9
prime radicalC3×D27C3
cosocleC3×C27C2×C3
LCSG ▷ C27
UCSC1 ◁ C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 54

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,4,3,5,7,6,8,9)(11,14)(12,18)(13,21)(15,16)(17,27)(19,20)(22,29)(23,28)(24,34)(25,33)(26,32)(30,31)(35,36);(10,29,23,30,34,32,12,11,33,13,36,27,19,16,15,20,17,35,21,25,14,18,26,24,31,28,22)

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×D27, C2×C9×D27, C27×D27, …
maximal normal subgroup ofD9×D27, C2×C9×D27, C27×D27, …
maximal quotient ofC9×Dic27, C2×C9×D27, C27×D27, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 13);