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C₂×D₃×#2002 #72247658

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

C₂×D₃×#2002

Splittings

Fitting	C₂×C₃×#2002 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#2002

Subgroups

	subgroup	G/H
center	C₂³	D₃×#120
commutator, cosocle	C₂²×C₃×C₄	C₂⁵
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₂×C₃×#2002	C₂
socle	C₂³×C₃	C₂×#120
hypercenter	C₂×#2002	D₃
hypocenter	C₃	C₂²×#2002
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#2002

21116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#23906, D₃×#394076
maximal normal subgroup of	C₂×D₃×#23906, D₃×#394076
maximal quotient of	D₃×#234591

GAP

Past the SmallGroups library coverage — no SmallGroups id.