C₁₉⋊C₃×D₁₁⋊C₂₅ #44535462

order	31350
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉⋊C₃×D₁₁⋊C₂₅
unambiguous semidirect product	D₁₁⋊(C₂₅×C₁₉⋊C₃)
unambiguous semidirect product	(C₁₁⋊C₂₅)⋊(C₂×C₁₉⋊C₃)
unambiguous semidirect product	(D₁₁×C₁₉⋊C₃)⋊C₂₅
unambiguous semidirect product	(C₁₉×D₁₁⋊C₂₅)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₁₉⋊C₃×AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁×C₁₉	C₂×C₃×C₂₅
Fitting, socle, cosocle	C₅×C₁₁×C₁₉	C₂×C₃×C₅
prime radical	C₅×D₁₁×C₁₉⋊C₃	C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₅

48 conjugacy classes of subgroups.

μ_t(G) = 5225

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 35);