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C₃×C₈×C₁₆×C₂₅ #72188305

order	9600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 81920
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₈

Aliases

abelian	C₃×C₈×C₁₆×C₂₅
multiplicative	(ℤ/10217)ˣ, (ℤ/20434)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₅×C₈	C₂²×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₄×C₅×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

312 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₈×C₂₅×C₃₂, C₃×C₁₆²×C₂₅, C₂×C₃×C₈×C₁₆×C₂₅, …
maximal normal subgroup of	C₃×C₈×C₂₅×C₃₂, C₃×C₁₆²×C₂₅, C₂×C₃×C₈×C₁₆×C₂₅, …
maximal quotient of	C₃×C₈×C₂₅×C₃₂, C₃×C₁₆²×C₂₅, C₂×C₃×C₈×C₁₆×C₂₅, …
automorphism group of	C₁₇×C₆₀₁
outer automorphism group of	C₁₇×C₆₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.