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C₂³×C₉×C₁₂₈ #72187960

order	9216
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4128768
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₉×C₁₂₈
multiplicative	(ℤ/27672)ˣ, (ℤ/29184)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₆₄	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₃×C₆₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

1119 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₉×C₂₅₆, C₂²×C₄×C₉×C₁₂₈, C₂⁴×C₉×C₁₂₈, …
maximal normal subgroup of	C₂³×C₉×C₂₅₆, C₂²×C₄×C₉×C₁₂₈, C₂⁴×C₉×C₁₂₈, …
maximal quotient of	C₂³×C₉×C₂₅₆, C₂²×C₄×C₉×C₁₂₈, C₂⁴×C₉×C₁₂₈, …
automorphism group of	C₃×C₈×C₁₁₅₃, C₃×C₁₉×C₅₁₂
outer automorphism group of	C₃×C₈×C₁₁₅₃, C₃×C₁₉×C₅₁₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.