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C₂×C₄²×C₈×C₉ #72182256

order	2304
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 37748736
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄³

Aliases

abelian	C₂×C₄²×C₈×C₉
multiplicative	(ℤ/5840)ˣ, (ℤ/5920)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃×C₄	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂²×C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

3069 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2304 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄²×C₉×C₁₆, C₂×C₄×C₈²×C₉, C₄³×C₈×C₉, …
maximal normal subgroup of	C₂×C₄²×C₉×C₁₆, C₂×C₄×C₈²×C₉, C₄³×C₈×C₉, …
maximal quotient of	C₂×C₄²×C₉×C₁₆, C₂×C₄×C₈²×C₉, C₄³×C₈×C₉, …
automorphism group of	C₅×C₁₆×C₇₃, C₅×C₃₂×C₃₇
outer automorphism group of	C₅×C₁₆×C₇₃, C₅×C₃₂×C₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.