Finite Group Databasebeta

← Prev (#72183272) Next (#72183274) →

C₂⁴×C₃²×C₂₅ #72183273

order	3600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 19353600
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

abelian	C₂⁴×C₃²×C₂₅
multiplicative	(ℤ/8456)ˣ, (ℤ/10872)ˣ, (ℤ/12684)ˣ

Subgroups

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

1206 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃²×C₄×C₂₅, C₂⁵×C₃²×C₂₅, C₂⁴×C₃×C₉×C₂₅, …
maximal normal subgroup of	C₂³×C₃²×C₄×C₂₅, C₂⁵×C₃²×C₂₅, C₂⁴×C₃×C₉×C₂₅, …
maximal quotient of	C₂³×C₃²×C₄×C₂₅, C₂⁵×C₃²×C₂₅, C₂⁴×C₃×C₉×C₂₅, …
automorphism group of	C₇×C₈×C₁₅₁, C₈×C₉×C₁₅₁
outer automorphism group of	C₇×C₈×C₁₅₁, C₈×C₉×C₁₅₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.