Finite Group Databasebeta

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C₂×D₃×#1390 #72248019

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁸

Aliases

C₂×D₃×#1390

Splittings

Fitting	C₂×C₃×#1390 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#1390

Subgroups

	subgroup	G/H
center	C₂³	D₃×#99
commutator	C₂³×C₃	C₂²×C₄²
Frattini	C₂²×D₄	C₂³×D₃
Fitting	C₂×C₃×#1390	C₂
socle	C₂³×C₃	C₂×#99
prime radical	C₂³×D₃×D₄	C₂²
cosocle	C₂²×C₃×D₄	C₂⁴
hypercenter	C₂×#1390	D₃
hypocenter	C₃	C₂²×#1390
LCS	G ▷ C₂³×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁴ ◁ C₂³×D₄ ◁ C₂×#1390

8268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#147555, D₃×#146654, D₃×#498931, …
maximal normal subgroup of	D₃×#147555, D₃×#146654, D₃×#498931, …
maximal quotient of	D₃×#128073

GAP

Past the SmallGroups library coverage — no SmallGroups id.