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Cayley diagram

C3×Dic36 #88457

order432
isoclinismisoclinic class of Dic36
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic36

Splittings

SylowC3×C9 ⋊ Q16

Subgroups

subgroupG/H
centerC2×C3D36
commutator, cosocleC4×C9C22×C3
FrattiniC3×C4C2×C3×D3
FittingC3×C8×C9C2
socle, prime radicalC2×C32D12
hypercenterC3×C8D9
hypocenterC9C3×Q16
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

62 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 144

A minimal faithful permutation representation — 2 generators on 28 points:

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

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11720234, #11720235, #11720240, …
maximal normal subgroup of#11720234, #11720235, #11720240, …
maximal quotient ofC3×#63376, C3×#63378, C2×C3×Dic36, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 104);