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C₂²×C₄×C₇²×C₉ #72186133

order	7056
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2322432
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₇

Aliases

abelian	C₂²×C₄×C₇²×C₉
multiplicative	(ℤ/11049)ˣ, (ℤ/14732)ˣ, (ℤ/22098)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂³×C₃×C₇²
socle, prime radical	C₂³×C₃×C₇²	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

810 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7056 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₇²×C₈×C₉, C₂×C₄²×C₇²×C₉, C₂³×C₄×C₇²×C₉, …
maximal normal subgroup of	C₂²×C₇²×C₈×C₉, C₂×C₄²×C₇²×C₉, C₂³×C₄×C₇²×C₉, …
maximal quotient of	C₂²×C₇²×C₈×C₉, C₂×C₄²×C₇²×C₉, C₂³×C₄×C₇²×C₉, …
automorphism group of	C₃×C₂₉×C₁₂₇
outer automorphism group of	C₃×C₂₉×C₁₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.