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C₂×C₇×C₉×C₄₇ #20238348

order	5922
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃²×C₂₃ (order 1656) · Inn(G) = C₁ · Out(G) = C₂³×C₃²×C₂₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₅₉₂₂
abelian	C₂×C₇×C₉×C₄₇
multiplicative	(ℤ/5923)ˣ, (ℤ/11846)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₃	C₂×C₃×C₇×C₄₇
socle	C₂×C₃×C₇×C₄₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5922 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₇×C₉×C₄₇, C₇×C₉×Dic₄₇, C₉×Dic₇×C₄₇, …
maximal normal subgroup of	C₄×C₇×C₉×C₄₇, C₇×C₉×Dic₄₇, C₉×Dic₇×C₄₇, …
maximal quotient of	C₄×C₇×C₉×C₄₇, C₂²×C₇×C₉×C₄₇, C₂×C₅×C₇×C₉×C₄₇, …
automorphism group of	C₅₉₂₃, C₂×C₅₉₂₃
outer automorphism group of	C₅₉₂₃, C₂×C₅₉₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5922, 1);