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C₄×C₁₉×C₁₅₁ #26039752

order	11476
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5400
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₄₇₆
abelian	C₄×C₁₉×C₁₅₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₉×C₁₅₁
socle, prime radical	C₂×C₁₉×C₁₅₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11476 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₁₄₇₆, D₂₂₉₅₂
Fitting subgroup of	C₄×C₁₉×C₁₅₁⋊C₃, C₄×C₁₉⋊C₃×C₁₅₁, C₄×#22575305, …
maximal subgroup of	C₃×C₄×C₁₉×C₁₅₁, C₄×C₁₉×C₁₅₁⋊C₃, C₄×C₁₉⋊C₃×C₁₅₁, …
maximal normal subgroup of	C₃×C₄×C₁₉×C₁₅₁, C₄×C₁₉×C₁₅₁⋊C₃, C₄×C₁₉⋊C₃×C₁₅₁, …
maximal quotient of	C₃×C₄×C₁₉×C₁₅₁, Dic₃×C₁₉×C₁₅₁, C₈×C₁₉×C₁₅₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11476, 1);