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C₂⁴×C₄×C₉×C₁₇ #72188508

order	9792
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 990904320
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

abelian	C₂⁴×C₄×C₉×C₁₇
multiplicative	(ℤ/36840)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂⁵×C₃×C₁₇
socle, prime radical	C₂⁵×C₃×C₁₇	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

4086 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9792 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₈×C₉×C₁₇, C₂³×C₄²×C₉×C₁₇, C₂⁵×C₄×C₉×C₁₇, …
maximal normal subgroup of	C₂⁴×C₈×C₉×C₁₇, C₂³×C₄²×C₉×C₁₇, C₂⁵×C₄×C₉×C₁₇, …
maximal quotient of	C₂⁴×C₈×C₉×C₁₇, C₂³×C₄²×C₉×C₁₇, C₂⁵×C₄×C₉×C₁₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.