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H(3,𝔽₃)×#634 #14518915

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₃³

Aliases

H(3,𝔽₃)×#634

Splittings

C₃²×H(3,𝔽₃) ⋊ Q₈

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₃	C₂×C₃²×C₃⋊D₃
commutator, socle, cosocle	C₂×C₃³	C₂²×C₃²
Fitting	C₃²×C₄×H(3,𝔽₃)	C₂
prime radical	C₂×C₃²×H(3,𝔽₃)	C₂²
hypercenter	C₄×H(3,𝔽₃)	C₃⋊D₃
hypocenter	C₃²	Q₈×H(3,𝔽₃)
LCS	G ▷ C₂×C₃³ ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₄×H(3,𝔽₃)

972 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 972 conjugacy classes of subgroups — too many to draw. Only its 147 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, 3309);