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C3×Dic6×3−1+2 #14518885

order1944
automorphism?
homologyAbelianization (H1) = C22×C33 · Schur multiplier (H2) = C32

Aliases

direct productC3×Dic6×3−1+2
unambiguous semidirect productC3⋊(C3×Q8×3−1+2)
unambiguous semidirect product(C9×Dic6)⋊C32

Splittings

SylowC32×3−1+2 ⋊ Q8

Subgroups

subgroupG/H
centerC2×C32C2×C32×D3
commutator, cosocleC2×C32C22×C33
FrattiniC2×C3C2×C33×D3
FittingC32×C4×3−1+2C2
socleC2×C33C22×C32
prime radicalC2×C34C22×C3
hypercenterC3×C4×3−1+2D3
hypocenterC3C3×Q8×3−1+2
LCSG ▷ C2×C32 ▷ C3
UCSC1 ◁ C2×C32 ◁ C3×C4×3−1+2

774 conjugacy classes of subgroups; only the 288 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 288 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) = 216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3279);