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3−1+2×GO+(4,𝔽2) #14519109

order1944
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2

Aliases

direct product3−1+2×GO+(4,𝔽2)
unambiguous semidirect product#157⋊(C2×3−1+2)
unambiguous semidirect productD32⋊(C2×3−1+2)
unambiguous semidirect product(C9×GO+(4,𝔽2))⋊C3

Splittings

Fitting, SylowC32×3−1+2 ⋊ D4

Subgroups

subgroupG/H
center, FrattiniC3C32×GO+(4,𝔽2)
commutator, cosocleC3×C3⋊D3C22×C32
FittingC32×3−1+2D4
socleC33C32×D4
prime radicalC32×GO+(4,𝔽2)C3
hypercenter3−1+2GO+(4,𝔽2)
hypocenterC32D4×3−1+2
LCSG ▷ C3×C3⋊D3 ▷ C32
UCSC1 ◁ C3 ◁ 3−1+2

304 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 49 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) = 36

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3503);