C₅×D₅×C₁₇×D₉ #29505797

order	15300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₅×C₁₇×D₉
unambiguous semidirect product	(C₅×D₉)⋊(C₂×C₅×C₁₇)
unambiguous semidirect product	(C₉×D₅)⋊(C₂×C₅×C₁₇)
unambiguous semidirect product	D₄₅⋊(C₂×C₅×C₁₇)

	subgroup	G/H
center, hypercenter	C₅×C₁₇	D₅×D₉
commutator, cosocle, hypocenter	C₅×C₉	C₂²×C₅×C₁₇
Frattini	C₃	C₅×D₃×D₅×C₁₇
Fitting	C₅²×C₉×C₁₇	C₂²
socle	C₃×C₅²×C₁₇	C₂×D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₅×C₁₇

144 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

μ_t(G) = 1530

2040 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 183);