Finite Group Databasebeta

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C2×#63651⋊C3 #13143207

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

Aliases

direct productC2×#63651⋊C3
unambiguous semidirect product(C2×#63651)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C2×#101

Subgroups

subgroupG/H
centerC22#3752⋊C3
commutatorC22×C32C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC2×M16×H(3,𝔽3)C2
socleC22×C3C3×(C2×D3)⋊C4
prime radicalC23×H(3,𝔽3)C2×C4
cosocleC2×C32×C4C23×C3
hypercenterC2×M16(C3⋊D3)⋊C3
hypocenterC32C2×C3×#101
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

579 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 9270);