Finite Group Databasebeta

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C₂⁴×C₃×C₄×C₈×C₉ #72192052

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 18264348426240
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₃×C₄

Aliases

abelian	C₂⁴×C₃×C₄×C₈×C₉
multiplicative	(ℤ/61320)ˣ, (ℤ/63840)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₄	C₂⁶×C₃²
socle, prime radical	C₂⁶×C₃²	C₂×C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

187540 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×C₄×C₉×C₁₆, C₂⁴×C₃×C₈²×C₉, C₂³×C₃×C₄²×C₈×C₉, …
maximal normal subgroup of	C₂⁴×C₃×C₄×C₉×C₁₆, C₂⁴×C₃×C₈²×C₉, C₂³×C₃×C₄²×C₈×C₉, …
maximal quotient of	C₂⁴×C₃×C₄×C₉×C₁₆, C₂⁴×C₃×C₈²×C₉, C₂³×C₃×C₄²×C₈×C₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.