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Cayley diagram

C32×C3⋊Dic3 #66464

order324
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C32

Aliases

direct productC32×C3⋊Dic3
unambiguous semidirect productC3⋊(C32×Dic3)

Splittings

derivedC32 ⋊ C32×C4
SylowC34 ⋊ C4

Subgroups

subgroupG/H
center, hypercenterC2×C32C3⋊D3
commutator, hypocenterC32C32×C4
FrattiniC2C32×C3⋊D3
Fitting, socle, prime radicalC2×C34C2
cosocleC2×C32C2×C32
LCSG ▷ C32
UCSC1 ◁ C2×C32

284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 36

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

derived subgroup of#13049434, #13049435, #13049436, …
maximal subgroup ofC32×#622, C3×C3⋊#622, C3⋊(C3⋊#622), …
maximal normal subgroup ofC32×#622, C3×C3⋊#622, C3⋊(C3⋊#622), …
maximal quotient ofC32×C3⋊(C3⋊C8), C2×C32×C3⋊Dic3, C32×C3⋊Dic9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 156);