Finite Group Databasebeta

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C₂⁴×C₃×C₉×C₃₂ #72192017

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8918138880
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

abelian	C₂⁴×C₃×C₉×C₃₂
multiplicative	(ℤ/44232)ˣ, (ℤ/51072)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₁₆	C₂⁵×C₃²
socle, prime radical	C₂⁵×C₃²	C₃×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

16020 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	C₂⁴×C₃×C₉×C₆₄, C₂³×C₃×C₄×C₉×C₃₂, C₂⁵×C₃×C₉×C₃₂
maximal normal subgroup of	C₂⁴×C₃×C₉×C₆₄, C₂³×C₃×C₄×C₉×C₃₂, C₂⁵×C₃×C₉×C₃₂
maximal quotient of	C₂⁴×C₃×C₉×C₆₄, C₂³×C₃×C₄×C₉×C₃₂, C₂⁵×C₃×C₉×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.