C₅×C₁₉×5₋¹⁺² #26045181

order	11875
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₅³×C₁₉ · Schur multiplier (H₂) = C₅²

Aliases

direct product	C₅×C₁₉×5₋¹⁺²
unambiguous semidirect product	C₂₅⋊(C₅²×C₁₉)
unambiguous semidirect product	(C₁₉×C₂₅)⋊C₅²

	subgroup	G/H
center, socle	C₅²×C₁₉	C₅²
commutator, Frattini, cosocle	C₅	C₅³×C₁₉
prime radical	C₅³×C₁₉	C₅
LCS	G ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₅²×C₁₉ ◁ G

160 conjugacy classes of subgroups.

2755 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11875, 13);