Finite Group Databasebeta

← Prev (#14517295) Next (#14517297) →

H(3,𝔽₃)×Dic₁₈ #14517296

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₃²

Aliases

H(3,𝔽₃)×Dic₁₈

Splittings

C₉×H(3,𝔽₃) ⋊ Q₈

Subgroups

	subgroup	G/H
center	C₂×C₃	C₂×C₃²×D₉
commutator, cosocle	C₂×C₃×C₉	C₂²×C₃²
Frattini, socle	C₂×C₃²	C₂×C₃²×D₃
Fitting	C₄×C₉×H(3,𝔽₃)	C₂
prime radical	C₂×C₃×H(3,𝔽₃)	C₂×D₃
hypercenter	C₄×H(3,𝔽₃)	D₉
hypocenter	C₉	Q₈×H(3,𝔽₃)
LCS	G ▷ C₂×C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₄×H(3,𝔽₃)

300 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 216

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, 1690);