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C₂⁴×C₃×C₈×C₉ #72183133

order	3456
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2229534720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

abelian	C₂⁴×C₃×C₈×C₉
multiplicative	(ℤ/12264)ˣ, (ℤ/12768)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂⁵×C₃²
socle, prime radical	C₂⁵×C₃²	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

9880 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3456 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₃×C₉×C₁₆, C₂³×C₃×C₄×C₈×C₉, C₂⁵×C₃×C₈×C₉, …
maximal normal subgroup of	C₂⁴×C₃×C₉×C₁₆, C₂³×C₃×C₄×C₈×C₉, C₂⁵×C₃×C₈×C₉, …
maximal quotient of	C₂⁴×C₃×C₉×C₁₆, C₂³×C₃×C₄×C₈×C₉, C₂⁵×C₃×C₈×C₉, …
automorphism group of	C₃×C₇×C₈×C₇₃, C₃×C₇×C₁₉×C₃₂
outer automorphism group of	C₃×C₇×C₈×C₇₃, C₃×C₇×C₁₉×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.