Finite Group Databasebeta

← Prev (#13143113) Next (#13143115) →

C2×#63641⋊C3 #13143114

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×#63641⋊C3
unambiguous semidirect product(C2×#63641)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×(C3⋊D3)⋊C3
commutatorC2×C32C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC22×C8×H(3,𝔽3)C2
socleC23×C3C3×C4×D3
prime radicalC23×H(3,𝔽3)C2×C4
cosocleC2×C32×C4C23×C3
hypercenterC22×C8(C3⋊D3)⋊C3
hypocenterC32C2×C3×C4⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

559 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, 9177);