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C₂⁴×C₃×C₈×C₁₇ #72185663

order	6528
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 660602880
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

abelian	C₂⁴×C₃×C₈×C₁₇
multiplicative	(ℤ/23016)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁵×C₃×C₁₇
socle, prime radical	C₂⁵×C₃×C₁₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

3952 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₃×C₁₆×C₁₇, C₂⁵×C₃×C₈×C₁₇, C₂³×C₃×C₄×C₈×C₁₇, …
maximal normal subgroup of	C₂⁴×C₃×C₁₆×C₁₇, C₂⁵×C₃×C₈×C₁₇, C₂³×C₃×C₄×C₈×C₁₇, …
maximal quotient of	C₂⁴×C₃×C₁₆×C₁₇, C₂⁵×C₃×C₈×C₁₇, C₂³×C₃×C₄×C₈×C₁₇, …
automorphism group of	C₃×C₇×C₈×C₁₃₇
outer automorphism group of	C₃×C₇×C₈×C₁₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.