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C₄×C₁₉×C₁₃₇ #23780988

order	10412
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₈×C₉×C₁₇ (order 4896) · Inn(G) = C₁ · Out(G) = C₂²×C₈×C₉×C₁₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₄₁₂
abelian	C₄×C₁₉×C₁₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₉×C₁₃₇
socle, prime radical	C₂×C₁₉×C₁₃₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10412 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₄₁₂, D₂₀₈₂₄
Fitting subgroup of	C₄×C₁₉⋊C₃×C₁₃₇
maximal subgroup of	C₃×C₄×C₁₉×C₁₃₇, C₄×C₁₉⋊C₃×C₁₃₇, Dic₃×C₁₉×C₁₃₇, …
maximal normal subgroup of	C₃×C₄×C₁₉×C₁₃₇, C₄×C₁₉⋊C₃×C₁₃₇, C₈×C₁₉×C₁₃₇, …
maximal quotient of	C₃×C₄×C₁₉×C₁₃₇, Dic₃×C₁₉×C₁₃₇, C₈×C₁₉×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10412, 1);