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C₂⁴×C₃×C₁₉₁ #72187916

order	9168
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7660800
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂⁴×C₃×C₁₉₁
multiplicative	(ℤ/21448)ˣ, (ℤ/27576)ˣ, (ℤ/32172)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

268 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9168 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃×C₄×C₁₉₁, C₂⁵×C₃×C₁₉₁, C₂⁴×C₉×C₁₉₁, …
maximal normal subgroup of	C₂³×C₃×C₄×C₁₉₁, C₂⁵×C₃×C₁₉₁, C₂⁴×C₉×C₁₉₁, …
maximal quotient of	C₂³×C₃×C₄×C₁₉₁, C₂⁵×C₃×C₁₉₁, C₂⁴×C₉×C₁₉₁, …
automorphism group of	C₇×C₈×C₃₈₃, C₈×C₉×C₃₈₃
outer automorphism group of	C₇×C₈×C₃₈₃, C₈×C₉×C₃₈₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.