C₂×C₅×D₈₅₅ #30685626

order	17100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₈₅₅
unambiguous semidirect product	(C₂×C₅)⋊(C₅×D₁₇₁)
unambiguous semidirect product	(C₂×C₉)⋊(C₅×D₉₅)
unambiguous semidirect product	(C₂×C₁₉)⋊(C₅×D₄₅)

	subgroup	G/H
center, hypercenter	C₂×C₅	D₈₅₅
commutator, cosocle, hypocenter	C₅×C₉×C₁₉	C₂²×C₅
Frattini	C₃	C₂×C₅×D₂₈₅
Fitting	C₂×C₅²×C₉×C₁₉	C₂
socle	C₂×C₃×C₅²×C₁₉	D₃
LCS	G ▷ C₅×C₉×C₁₉
UCS	C₁ ◁ C₂×C₅

144 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

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

μ_t(G) = 3420

4290 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 263);