Finite Group Databasebeta

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C4×#3744⋊C3 #13141457

order1728
isoclinismisoclinic class of #3746⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productC4×#3744⋊C3
unambiguous semidirect product(C4×#3744)⋊C3

Splittings

FittingC4×C8×H(3,𝔽3) ⋊ C2
SylowH(3,𝔽3) ⋊ C4×SD16

Subgroups

subgroupG/H
centerC2×C4C4⋊((C3⋊D3)⋊C3)
commutatorC32×C4C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC4×C8×H(3,𝔽3)C2
socleC22×C3C2×C3×D12
prime radicalC2×C4⋊((C3⋊D3)⋊C3)C22
cosocleC2×C32×C4C23×C3
hypercenterC4×C8(C3⋊D3)⋊C3
hypocenterC32C3×C4×SD16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

471 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 7520);