Finite Group Databasebeta

C2×#11757429 #14516601

order1944
automorphism?
homologyAbelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×#11757429

Splittings

SylowC23 ⋊ #6875

Subgroups

subgroupG/H
centerC2×C3C9⋊(C22⋊C9)
commutatorC22×C9C2×C3×C9
FrattiniC3×C9C2×C3×A4
FittingC23×C27⋊C3C3
socleC23×C3C9⋊C9
prime radicalC23×C323−1+2
cosocleC22×C3×C9C2×C32
hypercenterC2×C27⋊C3A4
hypocenterC22C2×#6875
LCSG ▷ C22×C9 ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C3 ◁ C2×C3×C9 ◁ C2×C27⋊C3

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×A4×#6875, C2×#72229255
maximal normal subgroup ofC2×A4×#6875
maximal quotient ofC2×#72229255

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 995);