Finite Group Databasebeta

← Prev (#72249307) Next (#72249309) →

D₃×#128073 #72249308

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₃×#128073 ⋊ C₂
Sylow	C₃ ⋊ C₂×#128073

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#342
commutator	C₂⁴×C₃	C₂²×C₄²
Frattini	C₂³×D₄	C₂³×D₃
Fitting	C₃×#128073	C₂
socle	C₂²×C₃	C₂²×#342
prime radical	C₂⁴×D₃×D₄	C₂²
cosocle	C₂³×C₃×D₄	C₂⁴
hypercenter	#128073	D₃
hypocenter	C₃	C₂×#128073
LCS	G ▷ C₂⁴×C₃ ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂⁴×D₄ ◁ #128073

At least 10710 conjugacy classes of subgroups; only the 935 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72210462, D₃×#72213256, D₃×#72210479, …
maximal normal subgroup of	D₃×#72210462, D₃×#72213256, D₃×#72210479, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.