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C₂³×C₄×C₅²×C₉ #72186276

order	7200
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 61931520
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₅

Aliases

abelian	C₂³×C₄×C₅²×C₉
multiplicative	(ℤ/15675)ˣ, (ℤ/15928)ˣ, (ℤ/20900)ˣ, (ℤ/23892)ˣ, (ℤ/29700)ˣ, (ℤ/31350)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂⁴×C₃×C₅²
socle, prime radical	C₂⁴×C₃×C₅²	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

2832 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₅²×C₈×C₉, C₂²×C₄²×C₅²×C₉, C₂⁴×C₄×C₅²×C₉, …
maximal normal subgroup of	C₂³×C₅²×C₈×C₉, C₂²×C₄²×C₅²×C₉, C₂⁴×C₄×C₅²×C₉, …
maximal quotient of	C₂³×C₅²×C₈×C₉, C₂²×C₄²×C₅²×C₉, C₂⁴×C₄×C₅²×C₉, …
automorphism group of	C₈×C₁₁×C₁₈₁, C₄×C₁₁×C₂₅×C₂₇
outer automorphism group of	C₈×C₁₁×C₁₈₁, C₄×C₁₁×C₂₅×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.