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C₂²×C₃×C₄²×C₆₄ #72190652

order	12288
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 38654705664
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁷×C₄³

Aliases

abelian	C₂²×C₃×C₄²×C₆₄
multiplicative	(ℤ/46320)ˣ, (ℤ/49920)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃₂	C₂⁵×C₃
socle, prime radical	C₂⁵×C₃	C₂²×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

28470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₄²×C₁₂₈, C₂×C₃×C₄³×C₆₄, C₂²×C₃×C₄×C₈×C₆₄, …
maximal normal subgroup of	C₂²×C₃×C₄²×C₁₂₈, C₂×C₃×C₄³×C₆₄, C₂²×C₃×C₄×C₈×C₆₄, …
maximal quotient of	C₂²×C₃×C₄²×C₁₂₈, C₂×C₃×C₄³×C₆₄, C₂²×C₃×C₄×C₈×C₆₄, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.