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C₅×C₇×C₉×C₃₇ #26042873

order	11655
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5184
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₆₅₅
abelian	C₅×C₇×C₉×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅×C₇×C₃₇
socle, prime radical	C₃×C₅×C₇×C₃₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11655 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₁₆₅₅
Fitting subgroup of	C₅×C₇×C₉×D₃₇, C₅×C₉×D₇×C₃₇, C₅×C₉×D₂₅₉, …
maximal subgroup of	C₂×C₅×C₇×C₉×C₃₇, C₅×C₇×C₉×D₃₇, C₅×C₉×D₇×C₃₇, …
maximal normal subgroup of	C₂×C₅×C₇×C₉×C₃₇, C₅×C₇×C₉×D₃₇, C₅×C₉×D₇×C₃₇, …
maximal quotient of	C₂×C₅×C₇×C₉×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11655, 1);