Finite Group Databasebeta

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D₃×#496225 #72255154

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹¹

Aliases

Splittings

Fitting	C₃×#496225 ⋊ C₂
Sylow	C₃ ⋊ C₂×#496225

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₃×#99
commutator	C₂⁴×C₃	C₂⁴×C₄
Frattini	C₂²×D₄	C₂⁴×D₃
Fitting	C₃×#496225	C₂
socle	C₂²×C₃	C₂³×#99
prime radical	C₂×D₃×#2403	C₂
cosocle	C₂²×C₃×D₄	C₂⁵
hypercenter	#496225	D₃
hypocenter	C₃	C₂×#496225
LCS	G ▷ C₂⁴×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂⁴×D₄ ◁ #496225

At least 14080 conjugacy classes of subgroups; only the 1431 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72213256, D₃×#72210566, D₃×#72213274, …
maximal normal subgroup of	D₃×#72213256, D₃×#72210566, D₃×#72213274, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.