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C₂²×C₄×C₁₉×C₂₅ #72186540

order	7600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 69120
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₁₉×C₂₅
multiplicative	(ℤ/15208)ˣ, (ℤ/22812)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂³×C₅×C₁₉
socle, prime radical	C₂³×C₅×C₁₉	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₈×C₁₉×C₂₅, C₂×C₄²×C₁₉×C₂₅, C₂³×C₄×C₁₉×C₂₅, …
maximal normal subgroup of	C₂²×C₈×C₁₉×C₂₅, C₂×C₄²×C₁₉×C₂₅, C₂³×C₄×C₁₉×C₂₅, …
maximal quotient of	C₂²×C₈×C₁₉×C₂₅, C₂×C₄²×C₁₉×C₂₅, C₂³×C₄×C₁₉×C₂₅, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.