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C₂⁵×C₃×C₄×C₅² #72188324

order	9600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 19659541708800
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁵×C₅

Aliases

abelian	C₂⁵×C₃×C₄×C₅²
multiplicative	(ℤ/40920)ˣ, (ℤ/46200)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁶×C₃×C₅²
socle, prime radical	C₂⁶×C₃×C₅²	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

84416 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	C₂⁵×C₃×C₅²×C₈, C₂⁴×C₃×C₄²×C₅², C₂⁶×C₃×C₄×C₅², …
maximal normal subgroup of	C₂⁵×C₃×C₅²×C₈, C₂⁴×C₃×C₄²×C₅², C₂⁶×C₃×C₄×C₅², …
maximal quotient of	C₂⁵×C₃×C₅²×C₈, C₂⁴×C₃×C₄²×C₅², C₂⁶×C₃×C₄×C₅², …

GAP

Past the SmallGroups library coverage — no SmallGroups id.