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C₂×C₃²×C₄²×C₁₇ #72184306

order	4896
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1179648
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

abelian	C₂×C₃²×C₄²×C₁₇
multiplicative	(ℤ/6695)ˣ, (ℤ/13390)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂³×C₃²×C₁₇
socle, prime radical	C₂³×C₃²×C₁₇	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4896 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₄×C₈×C₁₇, C₃²×C₄³×C₁₇, C₂²×C₃²×C₄²×C₁₇, …
maximal normal subgroup of	C₂×C₃²×C₄×C₈×C₁₇, C₃²×C₄³×C₁₇, C₂²×C₃²×C₄²×C₁₇, …
maximal quotient of	C₂×C₃²×C₄×C₈×C₁₇, C₃²×C₄³×C₁₇, C₂²×C₃²×C₄²×C₁₇, …
automorphism group of	C₅×C₁₃×C₁₀₃
outer automorphism group of	C₅×C₁₃×C₁₀₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.