Finite Group Databasebeta

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C₄×C₇×C₁₉×C₂₇ #72192518

order	14364
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃×C₉² (order 3888) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃×C₉²
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₃₆₄
abelian	C₄×C₇×C₁₉×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂×C₃×C₇×C₁₉
socle, prime radical	C₂×C₃×C₇×C₁₉	C₂×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14364 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₄₃₆₄, D₂₈₇₂₈
Fitting subgroup of	D₁₄₃₆₄, Dic₇₁₈₂
maximal subgroup of	C₇×C₈×C₁₉×C₂₇, C₂×C₄×C₇×C₁₉×C₂₇, D₁₄₃₆₄, …
maximal normal subgroup of	C₇×C₈×C₁₉×C₂₇, C₂×C₄×C₇×C₁₉×C₂₇, D₁₄₃₆₄, …
maximal quotient of	C₇×C₈×C₁₉×C₂₇, C₂×C₄×C₇×C₁₉×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.