Dic₅×C₃₁₁⋊C₅ #44527353

order	31100
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₅×C₃₁₁⋊C₅
unambiguous semidirect product	(Dic₅×C₃₁₁)⋊C₅

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×C₃₁₁⋊C₅
commutator, hypocenter	C₅×C₃₁₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₅×C₃₁₁	C₂×C₅
prime radical	C₂×C₅×C₃₁₁⋊C₅	C₂
LCS	G ▷ C₅×C₃₁₁
UCS	C₁ ◁ C₂

32 conjugacy classes of subgroups.

μ_t(G) = 6220

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31100, 19);