C₅×D₇×C₁₇×D₉ #36339243

order	21420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₇×C₁₇×D₉
unambiguous semidirect product	(C₇×D₉)⋊(C₂×C₅×C₁₇)
unambiguous semidirect product	(C₉×D₇)⋊(C₂×C₅×C₁₇)
unambiguous semidirect product	D₆₃⋊(C₂×C₅×C₁₇)

	subgroup	G/H
center, hypercenter	C₅×C₁₇	D₇×D₉
commutator, cosocle, hypocenter	C₇×C₉	C₂²×C₅×C₁₇
Frattini	C₃	C₅×D₃×D₇×C₁₇
Fitting	C₅×C₇×C₉×C₁₇	C₂²
socle	C₃×C₅×C₇×C₁₇	C₂×D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₅×C₁₇

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

normal subgroups only

This group has 120 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) = 5355

2550 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 75);