Finite Group Databasebeta

← Prev (#13142599) Next (#13142601) →

C2×#63635⋊C3 #13142600

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

Aliases

direct productC2×#63635⋊C3
unambiguous semidirect product(C2×#63635)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C2×#106

Subgroups

subgroupG/H
centerC23#638⋊C3
commutatorC32×C4C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C4⋊C4×H(3,𝔽3)C2
socleC23×C3C3×#67
prime radicalC23×H(3,𝔽3)D4
cosocleC2×C32×C4C23×C3
hypercenterC2×C4⋊C4(C3⋊D3)⋊C3
hypocenterC32C2×C3×#106
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

547 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8663);