Finite Group Databasebeta

← Prev (#72189270) Next (#72189272) →

C₂×C₃²×C₄×C₁₄₉ #72189271

order	10728
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 56832
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂×C₃²×C₄×C₁₄₉
multiplicative	(ℤ/12523)ˣ, (ℤ/16101)ˣ, (ℤ/25046)ˣ, (ℤ/32202)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃²×C₁₄₉
socle, prime radical	C₂²×C₃²×C₁₄₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10728 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₈×C₁₄₉, C₃²×C₄²×C₁₄₉, C₂²×C₃²×C₄×C₁₄₉, …
maximal normal subgroup of	C₂×C₃²×C₈×C₁₄₉, C₃²×C₄²×C₁₄₉, C₂²×C₃²×C₄×C₁₄₉, …
maximal quotient of	C₂×C₃²×C₈×C₁₄₉, C₃²×C₄²×C₁₄₉, C₂²×C₃²×C₄×C₁₄₉, …
automorphism group of	C₇×C₁₇₈₉
outer automorphism group of	C₇×C₁₇₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.