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C₂³×C₄×C₁₃×C₁₇ #72186145

order	7072
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4128768
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₄×C₁₃×C₁₇
multiplicative	(ℤ/17720)ˣ, (ℤ/21264)ˣ, (ℤ/26580)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁴×C₁₃×C₁₇
socle, prime radical	C₂⁴×C₁₃×C₁₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

472 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₈×C₁₃×C₁₇, C₂²×C₄²×C₁₃×C₁₇, C₂⁴×C₄×C₁₃×C₁₇, …
maximal normal subgroup of	C₂³×C₈×C₁₃×C₁₇, C₂²×C₄²×C₁₃×C₁₇, C₂⁴×C₄×C₁₃×C₁₇, …
maximal quotient of	C₂³×C₈×C₁₃×C₁₇, C₂²×C₄²×C₁₃×C₁₇, C₂⁴×C₄×C₁₃×C₁₇, …
automorphism group of	C₅×C₈×C₄₄₃, C₃×C₁₆×C₄₄₃
outer automorphism group of	C₅×C₈×C₄₄₃, C₃×C₁₆×C₄₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.