Finite Group Databasebeta

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C₂²×C₄²×C₉×C₂₅ #72192570

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 17694720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₄²×C₉×C₂₅
multiplicative	(ℤ/28785)ˣ, (ℤ/29896)ˣ, (ℤ/30704)ˣ, (ℤ/37000)ˣ, (ℤ/38000)ˣ, (ℤ/38380)ˣ, (ℤ/43632)ˣ, (ℤ/44844)ˣ, (ℤ/54000)ˣ, (ℤ/54540)ˣ, (ℤ/55500)ˣ, (ℤ/57570)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃×C₅	C₂⁴×C₃×C₅
socle, prime radical	C₂⁴×C₃×C₅	C₂²×C₃×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

2241 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	C₂²×C₄×C₈×C₉×C₂₅, C₂×C₄³×C₉×C₂₅, C₂³×C₄²×C₉×C₂₅
maximal normal subgroup of	C₂²×C₄×C₈×C₉×C₂₅, C₂×C₄³×C₉×C₂₅, C₂³×C₄²×C₉×C₂₅
maximal quotient of	C₂²×C₄×C₈×C₉×C₂₅, C₂×C₄³×C₉×C₂₅, C₂³×C₄²×C₉×C₂₅
automorphism group of	C₈×C₃₇×C₁₀₁, C₁₆×C₁₉×C₁₀₁
outer automorphism group of	C₈×C₃₇×C₁₀₁, C₁₆×C₁₉×C₁₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.