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C₂²×C₃×C₄×C₁₇₉ #72187447

order	8592
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 68352
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₃×C₄×C₁₇₉
multiplicative	(ℤ/12565)ˣ, (ℤ/14001)ˣ, (ℤ/16155)ˣ, (ℤ/18668)ˣ, (ℤ/25130)ˣ, (ℤ/28002)ˣ, (ℤ/32310)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃×C₁₇₉
socle, prime radical	C₂³×C₃×C₁₇₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8592 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄²×C₁₇₉, C₂²×C₃×C₈×C₁₇₉, C₂³×C₃×C₄×C₁₇₉, …
maximal normal subgroup of	C₂×C₃×C₄²×C₁₇₉, C₂²×C₃×C₈×C₁₇₉, C₂³×C₃×C₄×C₁₇₉, …
maximal quotient of	C₂×C₃×C₄²×C₁₇₉, C₂²×C₃×C₈×C₁₇₉, C₂³×C₃×C₄×C₁₇₉, …
automorphism group of	C₅×C₇×C₃₅₉
outer automorphism group of	C₅×C₇×C₃₅₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.