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C₂₇×C₃₄₇ #22627337

order	9369
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₉×C₁₇₃ (order 6228) · Inn(G) = C₁ · Out(G) = C₂²×C₉×C₁₇₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₃₆₉
abelian	C₂₇×C₃₄₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₉	C₃×C₃₄₇
socle	C₃×C₃₄₇	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9369 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₃₆₉, C₂×D₉₃₆₉
maximal subgroup of	C₈₁×C₃₄₇, C₃×C₂₇×C₃₄₇, C₂₇⋊C₃×C₃₄₇, …
maximal normal subgroup of	C₈₁×C₃₄₇, C₃×C₂₇×C₃₄₇, C₂₇⋊C₃×C₃₄₇, …
maximal quotient of	C₈₁×C₃₄₇, C₃×C₂₇×C₃₄₇, C₂×C₂₇×C₃₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9369, 1);