Finite Group Databasebeta

← Prev (#72189502) Next (#72189504) →

C₂×C₄×C₁₃₆₉ #72189503

order	10952
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 10656
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₁₃₆₉
multiplicative	(ℤ/16431)ˣ, (ℤ/21908)ˣ, (ℤ/32862)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃₇	C₂²×C₃₇
socle, prime radical	C₂²×C₃₇	C₂×C₃₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10952 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₁₃₆₉, C₄²×C₁₃₆₉, C₂²×C₄×C₁₃₆₉
maximal normal subgroup of	C₂×C₈×C₁₃₆₉, C₄²×C₁₃₆₉, C₂²×C₄×C₁₃₆₉
maximal quotient of	C₂×C₈×C₁₃₆₉, C₄²×C₁₃₆₉, C₂²×C₄×C₁₃₆₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.