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H(3,𝔽3)×GO+(4,𝔽2) #14519108

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

Aliases

direct productH(3,𝔽3)×GO+(4,𝔽2)
unambiguous semidirect product#157⋊(C2×H(3,𝔽3))
unambiguous semidirect productD32⋊(C2×H(3,𝔽3))
unambiguous semidirect product(C32×GO+(4,𝔽2))⋊C3

Splittings

Fitting, SylowC32×H(3,𝔽3) ⋊ D4

Subgroups

subgroupG/H
center, FrattiniC3C32×GO+(4,𝔽2)
commutator, cosocleC3×C3⋊D3C22×C32
FittingC32×H(3,𝔽3)D4
socleC33C32×D4
hypercenterH(3,𝔽3)GO+(4,𝔽2)
hypocenterC32D4×H(3,𝔽3)
LCSG ▷ C3×C3⋊D3 ▷ C32
UCSC1 ◁ C3 ◁ H(3,𝔽3)

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

normal subgroups only

This group has 436 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, 3502);