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C₂⁴×C₅²×C₁₉ #72186544

order	7600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 174182400
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₅

Aliases

abelian	C₂⁴×C₅²×C₁₉
multiplicative	(ℤ/16808)ˣ, (ℤ/25212)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

1072 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	C₂³×C₄×C₅²×C₁₉, C₂⁵×C₅²×C₁₉, C₂⁴×C₃×C₅²×C₁₉
maximal normal subgroup of	C₂³×C₄×C₅²×C₁₉, C₂⁵×C₅²×C₁₉, C₂⁴×C₃×C₅²×C₁₉
maximal quotient of	C₂³×C₄×C₅²×C₁₉, C₂⁵×C₅²×C₁₉, C₂⁴×C₃×C₅²×C₁₉
automorphism group of	C₈×C₁₁×C₁₉₁
outer automorphism group of	C₈×C₁₁×C₁₉₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.