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C2×#63648⋊C3 #13143127

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

Aliases

direct productC2×#63648⋊C3
unambiguous semidirect product(C2×#63648)⋊C3

Splittings

FittingC22×C8×H(3,𝔽3) ⋊ C2
SylowH(3,𝔽3) ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C4⋊((C3⋊D3)⋊C3)
commutatorC32×C4C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC22×C8×H(3,𝔽3)C2
socleC23×C3C3×D12
prime radicalC22×C4⋊((C3⋊D3)⋊C3)C2
cosocleC2×C32×C4C23×C3
hypercenterC22×C8(C3⋊D3)⋊C3
hypocenterC32C2×C3×#102
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

783 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, 9190);