Finite Group Databasebeta

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C₂²×C₇×C₁₉×C₂₇ #72192521

order	14364
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 11664
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₇×C₁₉×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂²×C₃×C₇×C₁₉
socle, prime radical	C₂²×C₃×C₇×C₁₉	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₄×C₇×C₁₉×C₂₇, C₂³×C₇×C₁₉×C₂₇
maximal normal subgroup of	C₂×C₄×C₇×C₁₉×C₂₇, C₂³×C₇×C₁₉×C₂₇
maximal quotient of	C₂×C₄×C₇×C₁₉×C₂₇, C₂³×C₇×C₁₉×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.