Finite Group Databasebeta

← Prev (#72187999) Next (#72188001) →

C₂⁴×C₄×C₉×C₁₆ #72188000

order	9216
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2029372047360
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

abelian	C₂⁴×C₄×C₉×C₁₆
multiplicative	(ℤ/38760)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₈	C₂⁶×C₃
socle, prime radical	C₂⁶×C₃	C₂×C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

76479 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₄×C₉×C₃₂, C₂⁴×C₈×C₉×C₁₆, C₂³×C₄²×C₉×C₁₆, …
maximal normal subgroup of	C₂⁴×C₄×C₉×C₃₂, C₂⁴×C₈×C₉×C₁₆, C₂³×C₄²×C₉×C₁₆, …
maximal quotient of	C₂⁴×C₄×C₉×C₃₂, C₂⁴×C₈×C₉×C₁₆, C₂³×C₄²×C₉×C₁₆, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.