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C₇×C₁₆×C₁₂₅ #72192184

order	14000
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄²×C₂₅ (order 4800) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄²×C₂₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₀₀₀
abelian	C₇×C₁₆×C₁₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈×C₂₅	C₂×C₅×C₇
socle, prime radical	C₂×C₅×C₇	C₈×C₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14000 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₄₀₀₀, D₂₈₀₀₀
Fitting subgroup of	D₁₄₀₀₀, Dic₇₀₀₀
maximal subgroup of	C₇×C₃₂×C₁₂₅, C₂×C₇×C₁₆×C₁₂₅, D₁₄₀₀₀, …
maximal normal subgroup of	C₇×C₃₂×C₁₂₅, C₂×C₇×C₁₆×C₁₂₅, D₁₄₀₀₀, …
maximal quotient of	C₇×C₃₂×C₁₂₅, C₂×C₇×C₁₆×C₁₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.