C₅×C₇×D₉×D₁₇ #36339240

order	21420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₇×D₉×D₁₇
unambiguous semidirect product	(C₁₇×D₉)⋊(C₂×C₅×C₇)
unambiguous semidirect product	(C₉×D₁₇)⋊(C₂×C₅×C₇)
unambiguous semidirect product	D₁₅₃⋊(C₂×C₅×C₇)

	subgroup	G/H
center, hypercenter	C₅×C₇	D₉×D₁₇
commutator, cosocle, hypocenter	C₉×C₁₇	C₂²×C₅×C₇
Frattini	C₃	C₅×D₃×C₇×D₁₇
Fitting	C₅×C₇×C₉×C₁₇	C₂²
socle	C₃×C₅×C₇×C₁₇	C₂×D₃
LCS	G ▷ C₉×C₁₇
UCS	C₁ ◁ C₅×C₇

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

2100 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 72);