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C₂₇×C₂₈₃ #21439416

order	7641
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₉×C₄₇ (order 5076) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₉×C₄₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₆₄₁
abelian	C₂₇×C₂₈₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₉	C₃×C₂₈₃
socle	C₃×C₂₈₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7641 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	C₂×D₇₆₄₁, Dic₇₆₄₁
Fitting subgroup of	C₂₈₃⋊C₈₁, C₂₇×C₂₈₃⋊C₃, #37523952, …
maximal subgroup of	C₈₁×C₂₈₃, C₃×C₂₇×C₂₈₃, C₂₇⋊C₃×C₂₈₃, …
maximal normal subgroup of	C₈₁×C₂₈₃, C₃×C₂₇×C₂₈₃, C₂₇⋊C₃×C₂₈₃, …
maximal quotient of	C₈₁×C₂₈₃, C₃×C₂₇×C₂₈₃, C₂×C₂₇×C₂₈₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7641, 1);