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C₂²×C₄×C₅²×C₂₉ #72190041

order	11600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2580480
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₅

Aliases

abelian	C₂²×C₄×C₅²×C₂₉
multiplicative	(ℤ/16225)ˣ, (ℤ/32450)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₅²×C₂₉
socle, prime radical	C₂³×C₅²×C₂₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₅²×C₈×C₂₉, C₂×C₄²×C₅²×C₂₉, C₂³×C₄×C₅²×C₂₉
maximal normal subgroup of	C₂²×C₅²×C₈×C₂₉, C₂×C₄²×C₅²×C₂₉, C₂³×C₄×C₅²×C₂₉
maximal quotient of	C₂²×C₅²×C₈×C₂₉, C₂×C₄²×C₅²×C₂₉, C₂³×C₄×C₅²×C₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.