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C₃×C₉×C₃₄₉ #22627993

order	9423
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 37584
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃×C₉×C₃₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₃	C₃²×C₃₄₉
socle	C₃²×C₃₄₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	C₉×C₃₄₉⋊C₉, (C₃×C₃₄₉⋊C₃)⋊C₉, (C₃₄₉⋊C₉)⋊C₉, …
maximal subgroup of	C₉²×C₃₄₉, C₃²⋊C₉×C₃₄₉, C₉⋊C₉×C₃₄₉, …
maximal normal subgroup of	C₉²×C₃₄₉, C₃²⋊C₉×C₃₄₉, C₉⋊C₉×C₃₄₉, …
maximal quotient of	C₉²×C₃₄₉, C₃²⋊C₉×C₃₄₉, C₉⋊C₉×C₃₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9423, 2);