Finite Group Databasebeta

C2×#11757623 #14517686

order1944
automorphism?
homologyAbelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×#11757623

Splittings

Sylow#6903 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22×C27C3⋊D3
commutator, hypocenterH(3,𝔽3)C2×C4×C9
FrattiniC2×C9C2×C3×C3⋊D3
FittingC22×#6903C2
socleC22×C3C9×C3⋊D3
prime radicalC22×H(3,𝔽3)C2×C9
cosocleC2×#737C22×C3
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C22×C27

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2080);