Finite Group Databasebeta

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D₃×#12705 #72231713

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

Splittings

Fitting	C₃×#12705 ⋊ C₂
Sylow	C₃ ⋊ C₂×#12705

Subgroups

	subgroup	G/H
center	C₂	D₃×#1781
commutator	C₂⁴×C₃	C₂³×C₄
Frattini	C₂²×D₄	C₂³×D₃
Fitting	C₃×#12705	C₂
socle	C₂×C₃	C₂×#1781
prime radical	D₃×#3484	C₂
cosocle	C₂²×C₃×D₄	C₂⁴
hypercenter	#12705	D₃
hypocenter	C₃	C₂×#12705
LCS	G ▷ C₂⁴×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂³×D₄ ◁ #12705

8380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#511790, D₃×#139750, D₃×#133839, …
maximal normal subgroup of	D₃×#511790, D₃×#139750, D₃×#133839, …
maximal quotient of	D₃×#147567, #72252338, C₂×D₃×#12705

GAP

Past the SmallGroups library coverage — no SmallGroups id.