Finite Group Databasebeta

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D₃×#11394 #72270294

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

Aliases

Splittings

Fitting	C₃×#11394 ⋊ C₂
Sylow	C₃ ⋊ C₂×#11394

Subgroups

	subgroup	G/H
center	C₂²	D₃×#393
commutator	C₂⁴×C₃	C₂³×C₄
Frattini	C₂⁵	C₂³×D₃
Fitting	C₃×#11394	C₂
socle	C₂²×C₃	C₂×#393
prime radical	C₂⁵×D₃	C₂³
cosocle	C₂⁵×C₃	C₂⁴
hypercenter	#11394	D₃
hypocenter	C₃	C₂×#11394
LCS	G ▷ C₂⁴×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #11394

7172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#404015, D₃×#363953
maximal normal subgroup of	D₃×#404015, D₃×#363953

GAP

Past the SmallGroups library coverage — no SmallGroups id.