Finite Group Databasebeta

← Prev (#72190897) Next (#72190899) →

C₄²×C₁₆×C₄₉ #72190898

order	12544
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8257536
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

abelian	C₄²×C₁₆×C₄₉
multiplicative	(ℤ/16745)ˣ, (ℤ/33490)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₇×C₈	C₂³×C₇
socle, prime radical	C₂³×C₇	C₂²×C₇×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

837 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12544 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄²×C₃₂×C₄₉, C₄×C₈×C₁₆×C₄₉, C₂×C₄²×C₁₆×C₄₉
maximal normal subgroup of	C₄²×C₃₂×C₄₉, C₄×C₈×C₁₆×C₄₉, C₂×C₄²×C₁₆×C₄₉
maximal quotient of	C₄²×C₃₂×C₄₉, C₄×C₈×C₁₆×C₄₉, C₂×C₄²×C₁₆×C₄₉
automorphism group of	C₅×C₁₇×C₁₉₇
outer automorphism group of	C₅×C₁₇×C₁₉₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.