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C₂×C₃×C₈²×C₉ #72183123

order	3456
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2654208
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₃×C₈

Aliases

C₂×C₃×C₈²×C₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄²	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₃×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

1400 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3456 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₉×C₁₆, C₃×C₄×C₈²×C₉, C₂²×C₃×C₈²×C₉, …
maximal normal subgroup of	C₂×C₃×C₈×C₉×C₁₆, C₃×C₄×C₈²×C₉, C₂²×C₃×C₈²×C₉, …
maximal quotient of	C₂×C₃×C₈×C₉×C₁₆, C₃×C₄×C₈²×C₉, C₂²×C₃×C₈²×C₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.