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C₂×C₃²×C₁₉×C₂₅ #22555475

order	8550
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 17280
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₂×C₃²×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₅	C₂×C₃²×C₅×C₁₉
socle	C₂×C₃²×C₅×C₁₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8550 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃²×C₂₅×Dic₁₉, C₃²×C₁₉×Dic₂₅, C₃²×Dic₄₇₅, …
maximal subgroup of	C₃²×C₄×C₁₉×C₂₅, C₃²×C₂₅×Dic₁₉, C₃²×C₁₉×Dic₂₅, …
maximal normal subgroup of	C₃²×C₄×C₁₉×C₂₅, C₃²×C₂₅×Dic₁₉, C₃²×C₁₉×Dic₂₅, …
maximal quotient of	C₃²×C₄×C₁₉×C₂₅, C₂²×C₃²×C₁₉×C₂₅, C₂×C₃×C₉×C₁₉×C₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 13);