Finite Group Databasebeta

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C₂×D₃×#3027 #72254578

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

C₂×D₃×#3027

Splittings

Fitting	C₂×C₃×#3027 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#3027

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#120
commutator, cosocle	C₂³×C₃	C₂⁶
Frattini	C₂³	C₂⁵×D₃
Fitting	C₂×C₃×#3027	C₂
socle	C₂²×C₃	C₂²×#120
hypercenter	C₂×#3027	D₃
hypocenter	C₃	C₂²×#3027
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#3027

46676 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#33553, D₃×#498888, D₃×#394076, …
maximal normal subgroup of	C₂×D₃×#33553, D₃×#498888, D₃×#394076, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.