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C₁₃×C₂₅×C₃₇ #26046675

order	12025
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₀₂₅
abelian	C₁₃×C₂₅×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₅×C₁₃×C₃₇
socle, prime radical	C₅×C₁₃×C₃₇	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12025 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₂₀₂₅
Fitting subgroup of	C₁₃×C₂₅×D₃₇, C₂₅×D₁₃×C₃₇, C₂₅×D₄₈₁, …
maximal subgroup of	C₂×C₁₃×C₂₅×C₃₇, C₁₃×C₂₅×D₃₇, C₂₅×D₁₃×C₃₇, …
maximal normal subgroup of	C₂×C₁₃×C₂₅×C₃₇, C₁₃×C₂₅×D₃₇, C₂₅×D₁₃×C₃₇, …
maximal quotient of	C₂×C₁₃×C₂₅×C₃₇, C₃×C₁₃×C₂₅×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12025, 1);