C₃²×D₅×D₇×C₁₇ #36339448

order	21420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₁₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃²×D₅×D₇×C₁₇

	subgroup	G/H
center, hypercenter	C₃²×C₁₇	D₅×D₇
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₃²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₃²×C₁₇

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

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

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

μ_t(G) = 5355

3060 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 280);