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C₃×C₇×C₁₉×C₂₅ #23756016

order	9975
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄×C₅×C₉ (order 4320) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄×C₅×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₉₇₅
abelian	C₃×C₇×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₃×C₅×C₇×C₁₉
socle, prime radical	C₃×C₅×C₇×C₁₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9975 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₉₉₇₅
Fitting subgroup of	C₃×C₇×C₂₅×D₁₉, C₃×D₇×C₁₉×C₂₅, C₃×C₂₅×D₁₃₃, …
maximal subgroup of	C₂×C₃×C₇×C₁₉×C₂₅, C₃×C₇×C₂₅×D₁₉, C₃×D₇×C₁₉×C₂₅, …
maximal normal subgroup of	C₂×C₃×C₇×C₁₉×C₂₅, C₃×C₇×C₂₅×D₁₉, C₃×D₇×C₁₉×C₂₅, …
maximal quotient of	C₂×C₃×C₇×C₁₉×C₂₅, C₇×C₉×C₁₉×C₂₅, C₃²×C₇×C₁₉×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9975, 1);