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C₃×C₄₉×C₇₉ #26042467

order	11613
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6552
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₆₁₃
abelian	C₃×C₄₉×C₇₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₃×C₇×C₇₉
socle, prime radical	C₃×C₇×C₇₉	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11613 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₁₆₁₃
Fitting subgroup of	C₃×C₄₉×D₇₉, C₃×C₇₉×D₄₉, C₃×D₃₈₇₁, …
maximal subgroup of	C₂×C₃×C₄₉×C₇₉, C₃×C₄₉×D₇₉, C₃×C₇₉×D₄₉, …
maximal normal subgroup of	C₂×C₃×C₄₉×C₇₉, C₃×C₄₉×D₇₉, C₃×C₇₉×D₄₉, …
maximal quotient of	C₂×C₃×C₄₉×C₇₉, C₉×C₄₉×C₇₉, C₃²×C₄₉×C₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11613, 1);