Finite Group Databasebeta

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C₃×C₄×C₈²×C₁₉ #72192732

order	14592
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 28311552
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄²×C₈

Aliases

C₃×C₄×C₈²×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄²	C₂³×C₃×C₁₉
socle, prime radical	C₂³×C₃×C₁₉	C₂×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

1500 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14592 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₈×C₁₆×C₁₉, C₃×C₈³×C₁₉, C₂×C₃×C₄×C₈²×C₁₉
maximal normal subgroup of	C₃×C₄×C₈×C₁₆×C₁₉, C₃×C₈³×C₁₉, C₂×C₃×C₄×C₈²×C₁₉
maximal quotient of	C₃×C₄×C₈×C₁₆×C₁₉, C₃×C₈³×C₁₉, C₂×C₃×C₄×C₈²×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.