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C₂⁵×C₃×C₈×C₉ #72186017

order	6912
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4423396884480
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁵×C₃

Aliases

C₂⁵×C₃×C₈×C₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂⁶×C₃²
socle, prime radical	C₂⁶×C₃²	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

77270 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6912 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁵×C₃×C₉×C₁₆, C₂⁴×C₃×C₄×C₈×C₉, C₂⁶×C₃×C₈×C₉, …
maximal normal subgroup of	C₂⁵×C₃×C₉×C₁₆, C₂⁴×C₃×C₄×C₈×C₉, C₂⁶×C₃×C₈×C₉, …
maximal quotient of	C₂⁵×C₃×C₉×C₁₆, C₂⁴×C₃×C₄×C₈×C₉, C₂⁶×C₃×C₈×C₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.