Finite Group Databasebeta

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C₂×D₃×#1790 #72247694

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹³

Aliases

C₂×D₃×#1790

Splittings

Fitting	C₂×C₃×#1790 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#1790

Subgroups

	subgroup	G/H
center	C₂³	D₃×#120
commutator	C₂³×C₃	C₂⁴×C₄
Frattini	C₂⁴	C₂⁴×D₃
Fitting	C₂×C₃×#1790	C₂
socle	C₂³×C₃	C₂×#120
prime radical	C₂²×D₃×H(5,𝔽₂)	C₂
cosocle	C₂⁴×C₃	C₂⁵
hypercenter	C₂×#1790	D₃
hypocenter	C₃	C₂²×#1790
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁵ ◁ C₂×#1790

40316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#394066, D₃×#498931, D₃×#494600, …
maximal normal subgroup of	D₃×#394066, D₃×#498931, D₃×#494600, …
maximal quotient of	C₂×D₃×#12753, D₃×#187928, C₂×D₃×#8534, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.