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C₂²×C₈²×C₉ #72182255

order	2304
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 14155776
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₈

Aliases

abelian	C₂²×C₈²×C₉
multiplicative	(ℤ/7008)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄²	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₃×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

2013 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	C₂²×C₈×C₉×C₁₆, C₂×C₄×C₈²×C₉, C₂³×C₈²×C₉, …
maximal normal subgroup of	C₂²×C₈×C₉×C₁₆, C₂×C₄×C₈²×C₉, C₂³×C₈²×C₉, …
maximal quotient of	C₂²×C₈×C₉×C₁₆, C₂×C₄×C₈²×C₉, C₂³×C₈²×C₉, …
automorphism group of	C₃×C₃₂×C₇₃
outer automorphism group of	C₃×C₃₂×C₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.