Finite Group Databasebeta

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C2×#63645⋊C3 #13143119

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×#63645⋊C3
unambiguous semidirect product(C2×#63645)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C2×#107

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 radicalC23×H(3,𝔽3)D4
cosocleC2×C32×C4C23×C3
hypercenterC22×C8(C3⋊D3)⋊C3
hypocenterC32C2×C3×#107
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

531 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

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, 9182);