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C₂×C₄²×C₁₆×C₁₇ #72187544

order	8704
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 201326592
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄³

Aliases

abelian	C₂×C₄²×C₁₆×C₁₇
multiplicative	(ℤ/23120)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₈	C₂⁴×C₁₇
socle, prime radical	C₂⁴×C₁₇	C₂²×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

2820 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8704 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄²×C₁₇×C₃₂, C₂×C₄×C₈×C₁₆×C₁₇, C₄³×C₁₆×C₁₇, …
maximal normal subgroup of	C₂×C₄²×C₁₇×C₃₂, C₂×C₄×C₈×C₁₆×C₁₇, C₄³×C₁₆×C₁₇, …
maximal quotient of	C₂×C₄²×C₁₇×C₃₂, C₂×C₄×C₈×C₁₆×C₁₇, C₄³×C₁₆×C₁₇, …
automorphism group of	C₅×C₁₆×C₂₈₉
outer automorphism group of	C₅×C₁₆×C₂₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.