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C₂₇×C₂₉₃ #21463665

order	7911
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄×C₉×C₇₃ (order 5256) · Inn(G) = C₁ · Out(G) = C₂×C₄×C₉×C₇₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₉₁₁
abelian	C₂₇×C₂₉₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₉	C₃×C₂₉₃
socle	C₃×C₂₉₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7911 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₇₉₁₁, C₂×D₇₉₁₁
maximal subgroup of	C₈₁×C₂₉₃, C₃×C₂₇×C₂₉₃, C₂₇⋊C₃×C₂₉₃, …
maximal normal subgroup of	C₈₁×C₂₉₃, C₃×C₂₇×C₂₉₃, C₂₇⋊C₃×C₂₉₃, …
maximal quotient of	C₈₁×C₂₉₃, C₃×C₂₇×C₂₉₃, C₂×C₂₇×C₂₉₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7911, 1);