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C₃×C₄²×C₁₃×C₂₅ #72193630

order	15600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 46080
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₃×C₄²×C₁₃×C₂₅
multiplicative	(ℤ/15857)ˣ, (ℤ/16913)ˣ, (ℤ/17069)ˣ, (ℤ/19625)ˣ, (ℤ/21125)ˣ, (ℤ/31714)ˣ, (ℤ/33826)ˣ, (ℤ/34138)ˣ, (ℤ/39250)ˣ, (ℤ/42250)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₅	C₂²×C₃×C₅×C₁₃
socle, prime radical	C₂²×C₃×C₅×C₁₃	C₂²×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₈×C₁₃×C₂₅, C₂×C₃×C₄²×C₁₃×C₂₅
maximal normal subgroup of	C₃×C₄×C₈×C₁₃×C₂₅, C₂×C₃×C₄²×C₁₃×C₂₅
maximal quotient of	C₃×C₄×C₈×C₁₃×C₂₅, C₂×C₃×C₄²×C₁₃×C₂₅
automorphism group of	C₁₀₁×C₁₅₇, C₁₃×C₁₃₀₁, C₁₂₅×C₁₆₉
outer automorphism group of	C₁₀₁×C₁₅₇, C₁₃×C₁₃₀₁, C₁₂₅×C₁₆₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.