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C₂×#11758013 #14518965

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂×#11758013

Splittings

H(5,𝔽₃) ⋊ C₂×C₄

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃	C₃²×C₃⋊D₃
commutator, hypocenter	H(3,𝔽₃)	C₂×C₃²×C₄
Frattini	C₂×C₃	C₂×C₃²×C₃⋊D₃
Fitting, prime radical	C₂²×H(5,𝔽₃)	C₂
cosocle	C₂×H(3,𝔽₃)	C₂²×C₃²
hypercenter	C₂²×H(3,𝔽₃)	C₃⋊D₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×H(3,𝔽₃)

1068 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 203 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

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3359);