Finite Group Databasebeta

← Prev (#13142406) Next (#13142408) →

C2×#63630⋊C3 #13142407

order1728
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×#63630⋊C3
unambiguous semidirect product(C2×#63630)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×(C3⋊D3)⋊C3
commutatorC2×C32C2×C3×C42
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C42×H(3,𝔽3)C2
socleC23×C3C2×C3×Dic3
prime radicalC23×H(3,𝔽3)C2×C4
cosocleC2×C32×C4C23×C3
hypercenterC2×C42(C3⋊D3)⋊C3
hypocenterC32C2×C3×#97
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

619 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8470);