C₂×C₅×C₁₉×D₈₅ #44568124

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

Aliases

direct product	C₂×C₅×C₁₉×D₈₅
unambiguous semidirect product	(C₂×C₅)⋊(C₅×C₁₉×D₁₇)
unambiguous semidirect product	(C₂×C₁₇)⋊(C₅×D₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₈₅
commutator, cosocle, hypocenter	C₅×C₁₇	C₂²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₇×C₁₉	C₂
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₂×C₅×C₁₉

96 conjugacy classes of subgroups.

μ_t(G) = 6460

8360 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32300, 113);