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C₂×C₃×C₄×C₁₉×C₂₅ #72189876

order	11400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5760
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₁₉×C₂₅
multiplicative	(ℤ/13307)ˣ, (ℤ/14255)ˣ, (ℤ/17103)ˣ, (ℤ/17109)ˣ, (ℤ/22804)ˣ, (ℤ/26614)ˣ, (ℤ/28510)ˣ, (ℤ/34206)ˣ, (ℤ/34218)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂²×C₃×C₅×C₁₉
socle, prime radical	C₂²×C₃×C₅×C₁₉	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₁₉×C₂₅, C₃×C₄²×C₁₉×C₂₅, C₂²×C₃×C₄×C₁₉×C₂₅
maximal normal subgroup of	C₂×C₃×C₈×C₁₉×C₂₅, C₃×C₄²×C₁₉×C₂₅, C₂²×C₃×C₄×C₁₉×C₂₅
maximal quotient of	C₂×C₃×C₈×C₁₉×C₂₅, C₃×C₄²×C₁₉×C₂₅, C₂²×C₃×C₄×C₁₉×C₂₅
automorphism group of	C₇×C₁₉₀₁, C₅×C₂₈₅₁
outer automorphism group of	C₇×C₁₉₀₁, C₅×C₂₈₅₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.