Finite Group Databasebeta

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D₃×#12062 #72245137

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₆ · Schur multiplier (H₂) = C₂⁶

Aliases

Splittings

Fitting	C₃×#12062 ⋊ C₂
Sylow	C₃ ⋊ C₂×#12062

Subgroups

	subgroup	G/H
center	C₂×C₈	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₁₆
Frattini	C₄×C₈	C₂³×D₃
Fitting	C₃×#12062	C₂
socle	C₂²×C₃	C₂×C₈×D₄
prime radical	C₂×D₃×D₈	C₈
cosocle	C₃×C₄×C₈	C₂⁴
hypercenter	#12062	D₃
hypocenter	C₃	C₂×#12062
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆ ◁ #12062

1180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 384

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×#122963
maximal normal subgroup of	D₃×#122963
maximal quotient of	D₃×#122963, D₃×#151103

GAP

Past the SmallGroups library coverage — no SmallGroups id.