Finite Group Databasebeta

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C₂⁵×C₃×C₄×C₉ #72183141

order	3456
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2211698442240
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁵×C₃

Aliases

abelian	C₂⁵×C₃×C₄×C₉
multiplicative	(ℤ/15960)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂⁶×C₃²
socle, prime radical	C₂⁶×C₃²	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

52760 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	C₂⁵×C₃×C₈×C₉, C₂⁴×C₃×C₄²×C₉, C₂⁶×C₃×C₄×C₉, …
maximal normal subgroup of	C₂⁵×C₃×C₈×C₉, C₂⁴×C₃×C₄²×C₉, C₂⁶×C₃×C₄×C₉, …
maximal quotient of	C₂⁵×C₃×C₈×C₉, C₂⁴×C₃×C₄²×C₉, C₂⁶×C₃×C₄×C₉, …
automorphism group of	C₃×C₅×C₇×C₈×C₁₉
outer automorphism group of	C₃×C₅×C₇×C₈×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.