C₁₉×D₁₇×C₅⋊D₅ #44568101

order	32300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₁₉×D₁₇×C₅⋊D₅
unambiguous semidirect product	(C₅×D₁₇)⋊(D₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₁₇×C₅⋊D₅
commutator, cosocle, hypocenter	C₅²×C₁₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₇×C₁₉	C₂²
LCS	G ▷ C₅²×C₁₇
UCS	C₁ ◁ C₁₉

160 conjugacy classes of subgroups.

μ_t(G) = 8075

2660 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32300, 90);