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C₂₅×C₃₄₉ #22576589

order	8725
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₃×C₄²×C₅×C₂₉ (order 6960) · Inn(G) = C₁ · Out(G) = C₃×C₄²×C₅×C₂₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₇₂₅
abelian	C₂₅×C₃₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₅	C₅×C₃₄₉
socle	C₅×C₃₄₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8725 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₈₇₂₅, Dic₈₇₂₅, #46853119, …
Fitting subgroup of	D₂₅×C₃₄₉, C₂₅×D₃₄₉, D₈₇₂₅, …
maximal subgroup of	C₂×C₂₅×C₃₄₉, D₂₅×C₃₄₉, C₂₅×D₃₄₉, …
maximal normal subgroup of	C₂×C₂₅×C₃₄₉, D₂₅×C₃₄₉, C₂₅×D₃₄₉, …
maximal quotient of	C₂×C₂₅×C₃₄₉, C₃×C₂₅×C₃₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8725, 1);