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C₂×C₈×C₉×C₄₉ #72186124

order	7056
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4032
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₈×C₉×C₄₉
multiplicative	(ℤ/10587)ˣ, (ℤ/14116)ˣ, (ℤ/21174)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄×C₇	C₂²×C₃×C₇
socle, prime radical	C₂²×C₃×C₇	C₃×C₄×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

99 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	C₂×C₉×C₁₆×C₄₉, C₄×C₈×C₉×C₄₉, C₂²×C₈×C₉×C₄₉, …
maximal normal subgroup of	C₂×C₉×C₁₆×C₄₉, C₄×C₈×C₉×C₄₉, C₂²×C₈×C₉×C₄₉, …
maximal quotient of	C₂×C₉×C₁₆×C₄₉, C₄×C₈×C₉×C₄₉, C₂²×C₈×C₉×C₄₉, …
automorphism group of	C₃×C₃₅₂₉
outer automorphism group of	C₃×C₃₅₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.