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C₂²×C₄×C₇×C₇₉ #72187696

order	8848
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 89856
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₇×C₇₉
multiplicative	(ℤ/17704)ˣ, (ℤ/26556)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₇×C₇₉
socle, prime radical	C₂³×C₇×C₇₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8848 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₇×C₈×C₇₉, C₂×C₄²×C₇×C₇₉, C₂³×C₄×C₇×C₇₉, …
maximal normal subgroup of	C₂²×C₇×C₈×C₇₉, C₂×C₄²×C₇×C₇₉, C₂³×C₄×C₇×C₇₉, …
maximal quotient of	C₂²×C₇×C₈×C₇₉, C₂×C₄²×C₇×C₇₉, C₂³×C₄×C₇×C₇₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.