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C₅×C₈×C₁₃×C₁₆ #72187239

order	8320
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 98304
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₈

Aliases

abelian	C₅×C₈×C₁₃×C₁₆
multiplicative	(ℤ/8857)ˣ, (ℤ/17714)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂²×C₅×C₁₃
socle, prime radical	C₂²×C₅×C₁₃	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

208 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₈×C₁₃×C₃₂, C₅×C₁₃×C₁₆², C₂×C₅×C₈×C₁₃×C₁₆, …
maximal normal subgroup of	C₅×C₈×C₁₃×C₃₂, C₅×C₁₃×C₁₆², C₂×C₅×C₈×C₁₃×C₁₆, …
maximal quotient of	C₅×C₈×C₁₃×C₃₂, C₅×C₁₃×C₁₆², C₂×C₅×C₈×C₁₃×C₁₆, …
automorphism group of	C₁₇×C₅₂₁
outer automorphism group of	C₁₇×C₅₂₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.