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C₄²×C₇²×C₁₆ #72190899

order	12544
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 396361728
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³×C₇

Aliases

abelian	C₄²×C₇²×C₁₆
multiplicative	(ℤ/16385)ˣ, (ℤ/32770)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₈	C₂³×C₇²
socle, prime radical	C₂³×C₇²	C₂²×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

2790 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×C₇²×C₃₂, C₄×C₇²×C₈×C₁₆, C₂×C₄²×C₇²×C₁₆
maximal normal subgroup of	C₄²×C₇²×C₃₂, C₄×C₇²×C₈×C₁₆, C₂×C₄²×C₇²×C₁₆
maximal quotient of	C₄²×C₇²×C₃₂, C₄×C₇²×C₈×C₁₆, C₂×C₄²×C₇²×C₁₆
automorphism group of	C₅×C₂₉×C₁₁₃
outer automorphism group of	C₅×C₂₉×C₁₁₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.