Finite Group Databasebeta

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D₃×#23882 #72214817

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

Splittings

Fitting	C₃×#23882 ⋊ C₂
Sylow	C₃ ⋊ C₂×#23882

Subgroups

	subgroup	G/H
center	C₂	D₃×#2403
commutator, cosocle	C₂²×C₃×C₄	C₂⁵
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₃×#23882	C₂
socle	C₂×C₃	C₂×#2403
hypercenter	#23882	D₃
hypocenter	C₃	C₂×#23882
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #23882

13620 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#511819, D₃×#511827, C₂×D₃×#23882, …
maximal normal subgroup of	D₃×#511819, D₃×#511827, C₂×D₃×#23882, …
maximal quotient of	#72214863, C₂×D₃×#23882, #72248597, …
automorphism group of	C₂×D₂₄, C₂×Dic₁₂
holomorph of	C₂×C₃×C₈

GAP

Past the SmallGroups library coverage — no SmallGroups id.