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SD16×(C3⋊Dic3)⋊C3 #13143362

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

Aliases

direct productSD16×(C3⋊Dic3)⋊C3
unambiguous semidirect product(SD16×C3⋊Dic3)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C4×SD16

Subgroups

subgroupG/H
centerC22D4×(C3⋊D3)⋊C3
commutatorC32×C4C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC2×SD16×H(3,𝔽3)C2
socleC22×C3C3×D3×D4
prime radicalC2×D4×H(3,𝔽3)C22
cosocleC2×C32×C4C23×C3
hypercenterC2×SD16(C3⋊D3)⋊C3
hypocenterC32C3×C4×SD16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

495 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

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, 9425);