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C₂²×C₄²×C₁₆₉ #72189381

order	10816
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 23003136
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₄²×C₁₆₉
multiplicative	(ℤ/27080)ˣ, (ℤ/32496)ˣ, (ℤ/40620)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₁₃	C₂⁴×C₁₃
socle, prime radical	C₂⁴×C₁₃	C₂²×C₁₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

747 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10816 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₈×C₁₆₉, C₂×C₄³×C₁₆₉, C₂³×C₄²×C₁₆₉, …
maximal normal subgroup of	C₂²×C₄×C₈×C₁₆₉, C₂×C₄³×C₁₆₉, C₂³×C₄²×C₁₆₉, …
maximal quotient of	C₂²×C₄×C₈×C₁₆₉, C₂×C₄³×C₁₆₉, C₂³×C₄²×C₁₆₉, …
automorphism group of	C₅×C₈×C₆₇₇, C₃×C₁₆×C₆₇₇
outer automorphism group of	C₅×C₈×C₆₇₇, C₃×C₁₆×C₆₇₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.