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Cayley diagram

C3⋊D32 #66477

order324
isoclinismisoclinic class of C3⋊D32
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C32

Aliases

direct productC3⋊D32

Splittings

Fitting, socle, derived, SylowC34 ⋊ C22

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC34C22
LCSG ▷ C34
UCSC1

356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 12
transitive degreeμt(G) = 18

A minimal faithful permutation representation — 3 generators on 12 points:

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

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC3×#72213247, C3×#72213277, #72252798, …
maximal subgroup ofC3⋊D3×#157, #10620197, #10620198, …
maximal normal subgroup ofC3⋊D3×#157, #10620197, #10620198, …
maximal quotient ofC3⋊D3×C3⋊Dic3, #10620150, #10620151, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 169);