Finite Group Databasebeta

← Prev (#72192170) Next (#72192172) →

C₁₉×C₂₃×C₃₂ #72192171

order	13984
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₈×C₉×C₁₁ (order 6336) · Inn(G) = C₁ · Out(G) = C₂³×C₈×C₉×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₉₈₄
abelian	C₁₉×C₂₃×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₁₉×C₂₃
socle, prime radical	C₂×C₁₉×C₂₃	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13984 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₉₈₄, D₂₇₉₆₈
Fitting subgroup of	D₁₃₉₈₄, Dic₆₉₉₂
maximal subgroup of	C₁₉×C₂₃×C₆₄, C₂×C₁₉×C₂₃×C₃₂, D₁₃₉₈₄, …
maximal normal subgroup of	C₁₉×C₂₃×C₆₄, C₂×C₁₉×C₂₃×C₃₂, D₁₃₉₈₄, …
maximal quotient of	C₁₉×C₂₃×C₆₄, C₂×C₁₉×C₂₃×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.