Finite Group Databasebeta

C2×#11720518 #13144231

order1728
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×#11720518

Splittings

FittingC2×C3×C42×C9 ⋊ C2
SylowC3×C9 ⋊ C2×#104

Subgroups

subgroupG/H
centerC2×C4C4⋊(C3⋊D9)
commutatorC3×C4×C9C22×C4
FrattiniC2×C3×C4C22×C3⋊D3
FittingC2×C3×C42×C9C2
socleC22×C32(C2×D3)⋊C4
prime radicalC2×#88736C2
cosocleC2×C3×C4×C9C23
hypercenterC2×C42C3⋊D9
hypocenterC3×C9C2×#104
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 432

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 10294);