C₃×C₇×D₅×D₅₁ #36339477

order	21420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₇×D₅×D₅₁
unambiguous semidirect product	(C₃×D₅)⋊(C₃×C₇×D₁₇)
unambiguous semidirect product	(D₅×C₁₇)⋊(C₃×D₃×C₇)

	subgroup	G/H
center, hypercenter	C₃×C₇	D₅×D₅₁
commutator, cosocle, hypocenter	C₃×C₅×C₁₇	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂²
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₃×C₇

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

μ_t(G) = 3570

2268 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 309);