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C₂²×C₉×C₂₃₉ #22575271

order	8604
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8568
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₉×C₂₃₉
multiplicative	(ℤ/9101)ˣ, (ℤ/12933)ˣ, (ℤ/18202)ˣ, (ℤ/25866)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₃	C₂²×C₃×C₂₃₉
socle	C₂²×C₃×C₂₃₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8604 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₉×C₂₃₉, C₂³×C₉×C₂₃₉, C₂²×C₂₇×C₂₃₉, …
maximal normal subgroup of	C₂×C₄×C₉×C₂₃₉, C₂³×C₉×C₂₃₉, C₂²×C₂₇×C₂₃₉, …
maximal quotient of	C₂×C₄×C₉×C₂₃₉, C₂³×C₉×C₂₃₉, C₂²×C₂₇×C₂₃₉, …
automorphism group of	C₁₉×C₄₇₉, C₂×C₂₇×C₄₇₉
outer automorphism group of	C₁₉×C₄₇₉, C₂×C₂₇×C₄₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8604, 5);