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C₂⁴×C₃×C₉×C₂₅ #72189358

order	10800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 43545600
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

abelian	C₂⁴×C₃×C₉×C₂₅
multiplicative	(ℤ/22952)ˣ, (ℤ/32616)ˣ, (ℤ/34428)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₅	C₂⁴×C₃²×C₅
socle, prime radical	C₂⁴×C₃²×C₅	C₃×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

2010 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃×C₄×C₉×C₂₅, C₂⁵×C₃×C₉×C₂₅, C₂⁴×C₃×C₂₅×C₂₇, …
maximal normal subgroup of	C₂³×C₃×C₄×C₉×C₂₅, C₂⁵×C₃×C₉×C₂₅, C₂⁴×C₃×C₂₅×C₂₇, …
maximal quotient of	C₂³×C₃×C₄×C₉×C₂₅, C₂⁵×C₃×C₉×C₂₅, C₂⁴×C₃×C₂₅×C₂₇, …
automorphism group of	C₈×C₁₉×C₁₅₁, C₈×C₂₇×C₁₅₁
outer automorphism group of	C₈×C₁₉×C₁₅₁, C₈×C₂₇×C₁₅₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.