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C₂³×D₃×#120 #72223813

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁷ · Schur multiplier (H₂) = C₂²²

Aliases

C₂³×D₃×#120

Splittings

Fitting	C₂³×C₃×#120 ⋊ C₂
Sylow	C₃ ⋊ C₂⁴×#120

Subgroups

	subgroup	G/H
center	C₂⁵	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁷
Frattini	C₂²	C₂⁶×D₃
Fitting	C₂³×C₃×#120	C₂
socle	C₂⁵×C₃	C₂⁴
hypercenter	C₂³×#120	D₃
hypocenter	C₃	C₂⁴×#120
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁵ ◁ C₂³×#120

563620 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×#394058, D₃×#846041, D₃×#647656, …
maximal normal subgroup of	D₃×#394058, D₃×#846041, D₃×#647656, …
maximal quotient of	C₂²×D₃×#3003, C₂×D₃×D₄×#120, D₃×#7630939, …
automorphism group of	#4550, C₈×Dic₆, #4679, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.