Finite Group Databasebeta

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C₂×C₃²×C₄×C₈×C₂₅ #72192560

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1966080
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

abelian	C₂×C₃²×C₄×C₈×C₂₅
multiplicative	(ℤ/21035)ˣ, (ℤ/23439)ˣ, (ℤ/27045)ˣ, (ℤ/31252)ˣ, (ℤ/42070)ˣ, (ℤ/46878)ˣ, (ℤ/54090)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₃²×C₅
socle, prime radical	C₂³×C₃²×C₅	C₂×C₄×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

1458 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	C₂×C₃²×C₄×C₁₆×C₂₅, C₂×C₃²×C₈²×C₂₅, C₃²×C₄²×C₈×C₂₅, …
maximal normal subgroup of	C₂×C₃²×C₄×C₁₆×C₂₅, C₂×C₃²×C₈²×C₂₅, C₃²×C₄²×C₈×C₂₅, …
maximal quotient of	C₂×C₃²×C₄×C₁₆×C₂₅, C₂×C₃²×C₈²×C₂₅, C₃²×C₄²×C₈×C₂₅, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.