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C₄×C₉×C₁₃×C₁₆ #72186453

order	7488
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 18432
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄×C₉×C₁₃×C₁₆
multiplicative	(ℤ/9365)ˣ, (ℤ/18730)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₈	C₂²×C₃×C₁₃
socle, prime radical	C₂²×C₃×C₁₃	C₂×C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7488 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₉×C₁₃×C₃₂, C₈×C₉×C₁₃×C₁₆, C₂×C₄×C₉×C₁₃×C₁₆, …
maximal normal subgroup of	C₄×C₉×C₁₃×C₃₂, C₈×C₉×C₁₃×C₁₆, C₂×C₄×C₉×C₁₃×C₁₆, …
maximal quotient of	C₄×C₉×C₁₃×C₃₂, C₈×C₉×C₁₃×C₁₆, C₂×C₄×C₉×C₁₃×C₁₆, …
automorphism group of	C₅×C₁₈₇₃
outer automorphism group of	C₅×C₁₈₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.