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C₃₂×C₃₅₉ #26039870

order	11488
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5728
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₄₈₈
abelian	C₃₂×C₃₅₉
multiplicative	(ℤ/11489)ˣ, (ℤ/22978)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₃₅₉
socle, prime radical	C₂×C₃₅₉	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11488 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃₅₉⋊C₆₄, C₃₂×D₃₅₉, #37526276, …
maximal subgroup of	C₆₄×C₃₅₉, C₂×C₃₂×C₃₅₉, M₆₄×C₃₅₉, …
maximal normal subgroup of	C₆₄×C₃₅₉, C₂×C₃₂×C₃₅₉, M₆₄×C₃₅₉, …
maximal quotient of	C₆₄×C₃₅₉, C₂×C₃₂×C₃₅₉
automorphism group of	C₁₁₄₈₉
outer automorphism group of	C₁₁₄₈₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11488, 1);