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C₂₅×C₄₄₉ #26014457

order	11225
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₂₂₅
abelian	C₂₅×C₄₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₅×C₄₄₉
socle, prime radical	C₅×C₄₄₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11225 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₁₂₂₅
Fitting subgroup of	D₂₅×C₄₄₉, C₂₅×D₄₄₉, D₁₁₂₂₅
maximal subgroup of	C₂×C₂₅×C₄₄₉, D₂₅×C₄₄₉, C₂₅×D₄₄₉, …
maximal normal subgroup of	C₂×C₂₅×C₄₄₉, D₂₅×C₄₄₉, C₂₅×D₄₄₉, …
maximal quotient of	C₂×C₂₅×C₄₄₉, C₃×C₂₅×C₄₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11225, 1);