Finite Group Databasebeta

← Prev (#72190261) Next (#72190263) →

C₄×C₈×C₉×C₄₁ #72190262

order	11808
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 30720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄×C₈×C₉×C₄₁
multiplicative	(ℤ/14765)ˣ, (ℤ/29530)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₄	C₂²×C₃×C₄₁
socle, prime radical	C₂²×C₃×C₄₁	C₂×C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11808 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₉×C₁₆×C₄₁, C₈²×C₉×C₄₁, C₂×C₄×C₈×C₉×C₄₁
maximal normal subgroup of	C₄×C₉×C₁₆×C₄₁, C₈²×C₉×C₄₁, C₂×C₄×C₈×C₉×C₄₁
maximal quotient of	C₄×C₉×C₁₆×C₄₁, C₈²×C₉×C₄₁, C₂×C₄×C₈×C₉×C₄₁
automorphism group of	C₅×C₂₉₅₃
outer automorphism group of	C₅×C₂₉₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.