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C₂×C₃×C₄×C₂₃×C₂₅ #72191975

order	13800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7040
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₂₃×C₂₅
multiplicative	(ℤ/14039)ˣ, (ℤ/14963)ˣ, (ℤ/17375)ˣ, (ℤ/28078)ˣ, (ℤ/29926)ˣ, (ℤ/34750)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂²×C₃×C₅×C₂₃
socle, prime radical	C₂²×C₃×C₅×C₂₃	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₂₃×C₂₅, C₃×C₄²×C₂₃×C₂₅, C₂²×C₃×C₄×C₂₃×C₂₅
maximal normal subgroup of	C₂×C₃×C₈×C₂₃×C₂₅, C₃×C₄²×C₂₃×C₂₅, C₂²×C₃×C₄×C₂₃×C₂₅
maximal quotient of	C₂×C₃×C₈×C₂₃×C₂₅, C₃×C₄²×C₂₃×C₂₅, C₂²×C₃×C₄×C₂₃×C₂₅
automorphism group of	C₁₀₁×C₁₃₉, C₁₃×C₁₁₅₁
outer automorphism group of	C₁₀₁×C₁₃₉, C₁₃×C₁₁₅₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.