Finite Group Databasebeta

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C₂⁵×C₃×C₉×C₁₆ #72192034

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8846793768960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁵×C₃

Aliases

abelian	C₂⁵×C₃×C₉×C₁₆
multiplicative	(ℤ/54264)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂⁶×C₃²
socle, prime radical	C₂⁶×C₃²	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

101780 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁵×C₃×C₉×C₃₂, C₂⁴×C₃×C₄×C₉×C₁₆, C₂⁶×C₃×C₉×C₁₆
maximal normal subgroup of	C₂⁵×C₃×C₉×C₃₂, C₂⁴×C₃×C₄×C₉×C₁₆, C₂⁶×C₃×C₉×C₁₆
maximal quotient of	C₂⁵×C₃×C₉×C₃₂, C₂⁴×C₃×C₄×C₉×C₁₆, C₂⁶×C₃×C₉×C₁₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.