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H(3,𝔽3)×Q8⋊C9 #14517238

order1944
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productH(3,𝔽3)×Q8⋊C9

Splittings

SylowQ8 ⋊ C9×H(3,𝔽3)

Subgroups

subgroupG/H
center, Frattini, socleC2×C32C32×A4
commutatorC3×Q8C32×C9
FittingC3×Q8×H(3,𝔽3)C3
prime radical, hypercenterC2×C3×H(3,𝔽3)A4
cosocleC32×Q8C33
hypocenterQ8C9×H(3,𝔽3)
LCSG ▷ C3×Q8 ▷ Q8
UCSC1 ◁ C2×C32 ◁ C2×C3×H(3,𝔽3)

359 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1632);