Finite Group Databasebeta

← Prev (#72185079) Next (#72185081) →

C₂×C₃⁴×C₄×C₉ #72185080

order	5832
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7640505999360
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃¹⁰

Aliases

C₂×C₃⁴×C₄×C₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃⁵
socle, prime radical	C₂²×C₃⁵	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

40928 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5832 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃⁴×C₈×C₉, C₃⁴×C₄²×C₉, C₂²×C₃⁴×C₄×C₉, …
maximal normal subgroup of	C₂×C₃⁴×C₈×C₉, C₃⁴×C₄²×C₉, C₂²×C₃⁴×C₄×C₉, …
maximal quotient of	C₂×C₃⁴×C₈×C₉, C₃⁴×C₄²×C₉, C₂²×C₃⁴×C₄×C₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.