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C₂×C₄×C₁₆×C₈₁ #72188995

order	10368
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 221184
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian	C₂×C₄×C₁₆×C₈₁
multiplicative	(ℤ/13855)ˣ, (ℤ/19455)ˣ, (ℤ/20655)ˣ, (ℤ/20752)ˣ, (ℤ/25940)ˣ, (ℤ/27710)ˣ, (ℤ/38910)ˣ, (ℤ/41310)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈×C₂₇	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂×C₈×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

540 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₃₂×C₈₁, C₂×C₈×C₁₆×C₈₁, C₄²×C₁₆×C₈₁, …
maximal normal subgroup of	C₂×C₄×C₃₂×C₈₁, C₂×C₈×C₁₆×C₈₁, C₄²×C₁₆×C₈₁, …
maximal quotient of	C₂×C₄×C₃₂×C₈₁, C₂×C₈×C₁₆×C₈₁, C₄²×C₁₆×C₈₁, …
automorphism group of	C₅×C₁₇×C₁₆₃, C₅×C₁₇×C₂₄₃
outer automorphism group of	C₅×C₁₇×C₁₆₃, C₅×C₁₇×C₂₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.