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C₂⁴×C₃×C₉×C₁₃ #72184881

order	5616
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 26127360
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

abelian	C₂⁴×C₃×C₉×C₁₃
multiplicative	(ℤ/12008)ˣ, (ℤ/17064)ˣ, (ℤ/18012)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂⁴×C₃²×C₁₃
socle, prime radical	C₂⁴×C₃²×C₁₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

1340 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃×C₄×C₉×C₁₃, C₂⁵×C₃×C₉×C₁₃, C₂⁴×C₉²×C₁₃, …
maximal normal subgroup of	C₂³×C₃×C₄×C₉×C₁₃, C₂⁵×C₃×C₉×C₁₃, C₂⁴×C₉²×C₁₃, …
maximal quotient of	C₂³×C₃×C₄×C₉×C₁₃, C₂⁵×C₃×C₉×C₁₃, C₂⁴×C₉²×C₁₃, …
automorphism group of	C₈×C₁₉×C₇₉, C₈×C₂₇×C₇₉
outer automorphism group of	C₈×C₁₉×C₇₉, C₈×C₂₇×C₇₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.