C₁₇×((C₅⋊D₅)⋊C₃)⋊D₇ #49087771

order	35700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₇×((C₅⋊D₅)⋊C₃)⋊D₇
unambiguous semidirect product	((C₅⋊D₅)⋊C₃)⋊(D₇×C₁₇)

	subgroup	G/H
center, hypercenter	C₁₇	((C₅⋊D₅)⋊C₃)⋊D₇
commutator, cosocle, hypocenter	C₇×C₅²⋊C₃	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₇	C₂×D₃
LCS	G ▷ C₇×C₅²⋊C₃
UCS	C₁ ◁ C₁₇

120 conjugacy classes of subgroups.

μ_t(G) = 1785

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 245);