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C3×Q8×AGL(1,𝔽9) #13180931

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×Q8×AGL(1,𝔽9)

Splittings

FittingC33×Q8 ⋊ C8
SylowC33 ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C3C22×AGL(1,𝔽9)
commutatorC2×C32C22×C3×C8
FrattiniC2C22×C3×AGL(1,𝔽9)
FittingC33×Q8C8
socleC2×C33C22×C8
prime radicalC2×C3×C3⋊D3C22×C4
cosocleC2×#157C23×C3
hypercenterC3×Q8AGL(1,𝔽9)
hypocenterC32C3×C8×Q8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×Q8

254 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 192

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46994);