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D3×A4×3−1+2 #14519241

order1944
automorphism?
homologyAbelianization (H1) = C2×C33 · Schur multiplier (H2) = C2×C32

Aliases

direct productD3×A4×3−1+2
unambiguous semidirect productC3⋊(C2×A4×3−1+2)

Splittings

FittingC22×C3×3−1+2 ⋊ C2×C3

Subgroups

subgroupG/H
center, FrattiniC3C32×D3×A4
commutator, socle, cosocleC22×C32C2×C33
FittingC22×C3×3−1+2C2×C3
prime radicalC32×D3×A4C3
hypercenter3−1+2D3×A4
hypocenterC22×C3C2×C3×3−1+2
LCSG ▷ C22×C32 ▷ C22×C3
UCSC1 ◁ C3 ◁ 3−1+2

591 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 591 conjugacy classes of subgroups — too many to draw. Only its 117 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) = 72

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3635);