Finite Group Databasebeta

← Prev (#24924257) Next (#24924259) →

C₃×C₄×C₁₉×C₄₇ #24924258

order	10716
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₉×C₂₃ (order 3312) · Inn(G) = C₁ · Out(G) = C₂⁴×C₉×C₂₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₇₁₆
abelian	C₃×C₄×C₁₉×C₄₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₁₉×C₄₇
socle, prime radical	C₂×C₃×C₁₉×C₄₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10716 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₇₁₆, D₂₁₄₃₂
Fitting subgroup of	C₄×C₄₇×#4294, C₃×C₄×C₄₇×C₁₉⋊C₃
maximal subgroup of	C₄×C₉×C₁₉×C₄₇, C₄×C₄₇×#4294, C₃²×C₄×C₁₉×C₄₇, …
maximal normal subgroup of	C₄×C₉×C₁₉×C₄₇, C₄×C₄₇×#4294, C₃²×C₄×C₁₉×C₄₇, …
maximal quotient of	C₄×C₉×C₁₉×C₄₇, C₃²×C₄×C₁₉×C₄₇, C₃×Dic₃×C₁₉×C₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10716, 1);