Finite Group Databasebeta

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C₈×C₉×C₂₂₇ #72194264

order	16344
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃×C₁₁₃ (order 5424) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃×C₁₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₃₄₄
abelian	C₈×C₉×C₂₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂×C₃×C₂₂₇
socle, prime radical	C₂×C₃×C₂₂₇	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16344 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₆₃₄₄, D₃₂₆₈₈
Fitting subgroup of	Dic₈₁₇₂, D₁₆₃₄₄
maximal subgroup of	C₉×C₁₆×C₂₂₇, C₂×C₈×C₉×C₂₂₇, Dic₈₁₇₂, …
maximal normal subgroup of	C₉×C₁₆×C₂₂₇, C₂×C₈×C₉×C₂₂₇, Dic₈₁₇₂, …
maximal quotient of	C₉×C₁₆×C₂₂₇, C₂×C₈×C₉×C₂₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.