Finite Group Databasebeta

← Prev (#72187457) Next (#72187459) →

C₂×C₃×C₄×C₃₅₉ #72187458

order	8616
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5728
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₃₅₉
multiplicative	(ℤ/9347)ˣ, (ℤ/18694)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₃₅₉
socle, prime radical	C₂²×C₃×C₃₅₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₃₅₉, C₃×C₄²×C₃₅₉, C₂²×C₃×C₄×C₃₅₉, …
maximal normal subgroup of	C₂×C₃×C₈×C₃₅₉, C₃×C₄²×C₃₅₉, C₂²×C₃×C₄×C₃₅₉, …
maximal quotient of	C₂×C₃×C₈×C₃₅₉, C₃×C₄²×C₃₅₉, C₂²×C₃×C₄×C₃₅₉, …
automorphism group of	C₁₃×C₇₁₉
outer automorphism group of	C₁₃×C₇₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.