Finite Group Databasebeta

C2×#11757860 #14518446

order1944
automorphism?
homologyAbelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C2×C32

Aliases

direct productC2×#11757860

Splittings

SylowC23 ⋊ #6903

Subgroups

subgroupG/H
centerC2×C9C32×A4
commutatorC22×C3C2×C32×C9
FrattiniC9C2×C32×A4
FittingC23×#737C3
socleC23×C3C32×C9
prime radicalC23×H(3,𝔽3)C9
cosocleC22×C9C2×C33
hypercenterC2×#737A4
hypocenterC22C2×#6903
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C9 ◁ C2×#737

352 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2840);