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C₃×C₄²×C₇×C₂₅ #72187282

order	8400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 23040
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₃×C₄²×C₇×C₂₅
multiplicative	(ℤ/9113)ˣ, (ℤ/18226)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₅	C₂²×C₃×C₅×C₇
socle, prime radical	C₂²×C₃×C₅×C₇	C₂²×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₇×C₈×C₂₅, C₂×C₃×C₄²×C₇×C₂₅, C₄²×C₇×C₉×C₂₅, …
maximal normal subgroup of	C₃×C₄×C₇×C₈×C₂₅, C₂×C₃×C₄²×C₇×C₂₅, C₄²×C₇×C₉×C₂₅, …
maximal quotient of	C₃×C₄×C₇×C₈×C₂₅, C₂×C₃×C₄²×C₇×C₂₅, C₄²×C₇×C₉×C₂₅, …
automorphism group of	C₁₃×C₇₀₁
outer automorphism group of	C₁₃×C₇₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.