Finite Group Databasebeta

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D₃×#496124 #72258591

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

Splittings

Fitting	C₃×#496124 ⋊ C₂
Sylow	C₃ ⋊ C₂×#496124

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#442
commutator	C₂×C₃×C₈	C₂⁴×C₄
Frattini	C₂²×C₈	C₂⁴×D₃
Fitting	C₃×#496124	C₂
socle	C₂²×C₃	C₂²×#442
prime radical	D₃×#33717	C₂
cosocle	C₂²×C₃×C₈	C₂⁵
hypercenter	#496124	D₃
hypocenter	C₃	C₂×#496124
LCS	G ▷ C₂×C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#97 ◁ #496124

10382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.