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C₂₇×C₃₄₉ #22627992

order	9423
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄×C₉×C₂₉ (order 6264) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄×C₉×C₂₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₄₂₃
abelian	C₂₇×C₃₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₉	C₃×C₃₄₉
socle	C₃×C₃₄₉	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9423 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₄₂₃, C₂×D₉₄₂₃
Fitting subgroup of	C₃₄₉⋊C₈₁, C₂₇×C₃₄₉⋊C₃, #43246502, …
maximal subgroup of	C₈₁×C₃₄₉, C₃×C₂₇×C₃₄₉, C₂₇⋊C₃×C₃₄₉, …
maximal normal subgroup of	C₈₁×C₃₄₉, C₃×C₂₇×C₃₄₉, C₂₇⋊C₃×C₃₄₉, …
maximal quotient of	C₈₁×C₃₄₉, C₃×C₂₇×C₃₄₉, C₂×C₂₇×C₃₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9423, 1);