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C₂³×C₃²×C₄₉ #72183192

order	3528
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 338688
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃

Aliases

abelian	C₂³×C₃²×C₄₉
multiplicative	(ℤ/12348)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₂³×C₃²×C₇
socle, prime radical	C₂³×C₃²×C₇	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

288 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃²×C₄×C₄₉, C₂⁴×C₃²×C₄₉, C₂³×C₃×C₉×C₄₉, …
maximal normal subgroup of	C₂²×C₃²×C₄×C₄₉, C₂⁴×C₃²×C₄₉, C₂³×C₃×C₉×C₄₉, …
maximal quotient of	C₂²×C₃²×C₄×C₄₉, C₂⁴×C₃²×C₄₉, C₂³×C₃×C₉×C₄₉, …
automorphism group of	C₄×C₉×C₃₄₃
outer automorphism group of	C₄×C₉×C₃₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.