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C₂⁵×C₁₆×C₁₉ #72188443

order	9728
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1474465628160
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁵

Aliases

C₂⁵×C₁₆×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂⁶×C₁₉
socle, prime radical	C₂⁶×C₁₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20356 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9728 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁵×C₁₉×C₃₂, C₂⁴×C₄×C₁₆×C₁₉, C₂⁶×C₁₆×C₁₉, …
maximal normal subgroup of	C₂⁵×C₁₉×C₃₂, C₂⁴×C₄×C₁₆×C₁₉, C₂⁶×C₁₆×C₁₉, …
maximal quotient of	C₂⁵×C₁₉×C₃₂, C₂⁴×C₄×C₁₆×C₁₉, C₂⁶×C₁₆×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.