Finite Group Databasebeta

← Prev (#72192545) Next (#72192547) →

C₄×C₉×C₁₆×C₂₅ #72192546

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 30720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄×C₉×C₁₆×C₂₅
multiplicative	(ℤ/14837)ˣ, (ℤ/29674)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₅×C₈	C₂²×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₂×C₃×C₅×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

261 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₉×C₂₅×C₃₂, C₈×C₉×C₁₆×C₂₅, C₂×C₄×C₉×C₁₆×C₂₅
maximal normal subgroup of	C₄×C₉×C₂₅×C₃₂, C₈×C₉×C₁₆×C₂₅, C₂×C₄×C₉×C₁₆×C₂₅
maximal quotient of	C₄×C₉×C₂₅×C₃₂, C₈×C₉×C₁₆×C₂₅, C₂×C₄×C₉×C₁₆×C₂₅
automorphism group of	C₃₇×C₄₀₁
outer automorphism group of	C₃₇×C₄₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.