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C₂²×C₁₉×C₁₂₅ #72188231

order	9500
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 10800
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₁₉×C₁₂₅
multiplicative	(ℤ/14253)ˣ, (ℤ/19004)ˣ, (ℤ/28506)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₅	C₂²×C₅×C₁₉
socle, prime radical	C₂²×C₅×C₁₉	C₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9500 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₁₉×C₁₂₅, C₂³×C₁₉×C₁₂₅, C₂²×C₃×C₁₉×C₁₂₅
maximal normal subgroup of	C₂×C₄×C₁₉×C₁₂₅, C₂³×C₁₉×C₁₂₅, C₂²×C₃×C₁₉×C₁₂₅
maximal quotient of	C₂×C₄×C₁₉×C₁₂₅, C₂³×C₁₉×C₁₂₅, C₂²×C₃×C₁₉×C₁₂₅
automorphism group of	C₃×C₄₇₅₁
outer automorphism group of	C₃×C₄₇₅₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.