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C₂×C₄²×C₃₄₃ #72189529

order	10976
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 451584
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian	C₂×C₄²×C₃₄₃
multiplicative	(ℤ/20595)ˣ, (ℤ/21968)ˣ, (ℤ/27460)ˣ, (ℤ/41190)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄₉	C₂³×C₇
socle, prime radical	C₂³×C₇	C₂²×C₄₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10976 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₈×C₃₄₃, C₄³×C₃₄₃, C₂²×C₄²×C₃₄₃
maximal normal subgroup of	C₂×C₄×C₈×C₃₄₃, C₄³×C₃₄₃, C₂²×C₄²×C₃₄₃
maximal quotient of	C₂×C₄×C₈×C₃₄₃, C₄³×C₃₄₃, C₂²×C₄²×C₃₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.