C₁₇×(C₅⋊AGL(1,𝔽₇))⋊D₅ #49087805

order	35700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₇×(C₅⋊AGL(1,𝔽₇))⋊D₅
unambiguous semidirect product	(C₅⋊AGL(1,𝔽₇))⋊(D₅×C₁₇)
unambiguous semidirect product	((C₅⋊D₅)⋊D₇)⋊(C₃×C₁₇)
unambiguous semidirect product	(C₁₇×(C₅⋊D₅)⋊D₇)⋊C₃

	subgroup	G/H
center, hypercenter	C₁₇	(C₅⋊AGL(1,𝔽₇))⋊D₅
commutator, cosocle, hypocenter	C₅²×C₇	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₇	C₂²×C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₁₇

192 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 1190

1054 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 279);