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C₂×C₄×C₂₅×C₅₃ #72189179

order	10600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8320
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₂₅×C₅₃
multiplicative	(ℤ/10807)ˣ, (ℤ/13375)ˣ, (ℤ/21614)ˣ, (ℤ/26750)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂²×C₅×C₅₃
socle, prime radical	C₂²×C₅×C₅₃	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₂₅×C₅₃, C₄²×C₂₅×C₅₃, C₂²×C₄×C₂₅×C₅₃, …
maximal normal subgroup of	C₂×C₈×C₂₅×C₅₃, C₄²×C₂₅×C₅₃, C₂²×C₄×C₂₅×C₅₃, …
maximal quotient of	C₂×C₈×C₂₅×C₅₃, C₄²×C₂₅×C₅₃, C₂²×C₄×C₂₅×C₅₃, …
automorphism group of	C₁₀₁×C₁₀₇, C₂×C₁₀₇×C₁₂₅
outer automorphism group of	C₁₀₁×C₁₀₇, C₂×C₁₀₇×C₁₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.