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C3×Q8×GO+(4,𝔽2) #13181042

order1728
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×Q8×GO+(4,𝔽2)

Splittings

FittingC33×Q8 ⋊ D4
SylowC33 ⋊ D4×Q8

Subgroups

subgroupG/H
centerC2×C3C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊D3C24×C3
FrattiniC2C22×C3×GO+(4,𝔽2)
FittingC33×Q8D4
socleC2×C33C22×D4
prime radicalC2×C3×GO+(4,𝔽2)C22
hypercenterC3×Q8GO+(4,𝔽2)
hypocenterC32C3×D4×Q8
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×Q8

948 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 194 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) = 96

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, 47105);