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C₂³×C₃×C₄×C₈² #72185336

order	6144
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 69269232549888
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹²×C₄²×C₈

Aliases

C₂³×C₃×C₄×C₈²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄²	C₂⁶×C₃
socle, prime radical	C₂⁶×C₃	C₂×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

215504 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6144 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃×C₄×C₈×C₁₆, C₂³×C₃×C₈³, C₂²×C₃×C₄²×C₈², …
maximal normal subgroup of	C₂³×C₃×C₄×C₈×C₁₆, C₂³×C₃×C₈³, C₂²×C₃×C₄²×C₈², …
maximal quotient of	C₂³×C₃×C₄×C₈×C₁₆, C₂³×C₃×C₈³, C₂²×C₃×C₄²×C₈², …

GAP

Past the SmallGroups library coverage — no SmallGroups id.