Finite Group Databasebeta

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#102×(C3⋊D3)⋊C3 #13141786

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C3

Aliases

direct product#102×(C3⋊D3)⋊C3
unambiguous semidirect product(C3⋊D3×#102)⋊C3

Splittings

FittingH(3,𝔽3)×#102 ⋊ C2
SylowH(3,𝔽3) ⋊ C2×#102

Subgroups

subgroupG/H
centerC22D4×(C3⋊D3)⋊C3
commutatorC32×C4C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingH(3,𝔽3)×#102C2
socleC22×C3C3×D3×D4
prime radicalC2×D4×(C3⋊D3)⋊C3C2
cosocleC2×C32×C4C23×C3
hypercenter#102(C3⋊D3)⋊C3
hypocenterC32C2×C3×#102
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

757 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 7849);