C₂×C₅⋊D₅×C₃₁₃ #44531050

order	31300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃₁₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₅⋊D₅×C₃₁₃
unambiguous semidirect product	(C₂×C₅)⋊(D₅×C₃₁₃)

	subgroup	G/H
center, hypercenter	C₂×C₃₁₃	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₃₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₃₁₃	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃₁₃

80 conjugacy classes of subgroups.

μ_t(G) = 15650

8764 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31300, 49);