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C₂×C₃²×C₄×C₄₉ #72183188

order	3528
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 16128
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂×C₃²×C₄×C₄₉
multiplicative	(ℤ/4459)ˣ, (ℤ/8918)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₇	C₂²×C₃²×C₇
socle, prime radical	C₂²×C₃²×C₇	C₂×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

144 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	C₂×C₃²×C₈×C₄₉, C₃²×C₄²×C₄₉, C₂²×C₃²×C₄×C₄₉, …
maximal normal subgroup of	C₂×C₃²×C₈×C₄₉, C₃²×C₄²×C₄₉, C₂²×C₃²×C₄×C₄₉, …
maximal quotient of	C₂×C₃²×C₈×C₄₉, C₃²×C₄²×C₄₉, C₂²×C₃²×C₄×C₄₉, …
automorphism group of	C₁₃×C₃₄₃, C₂×C₁₃×C₃₄₃
outer automorphism group of	C₁₃×C₃₄₃, C₂×C₁₃×C₃₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.