Finite Group Databasebeta

← Prev (#24926361) Next (#24926363) →

C₁₉×C₂₃×C₂₅ #24926362

order	10925
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₅×C₉×C₁₁ (order 7920) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₅×C₉×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₉₂₅
abelian	C₁₉×C₂₃×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₅×C₁₉×C₂₃
socle, prime radical	C₅×C₁₉×C₂₃	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10925 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₀₉₂₅
Fitting subgroup of	C₁₉×C₂₅×D₂₃, C₂₃×C₂₅×D₁₉, C₂₅×D₄₃₇, …
maximal subgroup of	C₂×C₁₉×C₂₃×C₂₅, C₁₉×C₂₅×D₂₃, C₂₃×C₂₅×D₁₉, …
maximal normal subgroup of	C₂×C₁₉×C₂₃×C₂₅, C₁₉×C₂₅×D₂₃, C₂₃×C₂₅×D₁₉, …
maximal quotient of	C₂×C₁₉×C₂₃×C₂₅, C₃×C₁₉×C₂₃×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10925, 1);