C₇×D₂₁×D₆₅ #50304457

order	38220
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

C₇×D₂₁×D₆₅

	subgroup	G/H
center, hypercenter	C₇	D₂₁×D₆₅
commutator, cosocle, hypocenter	C₃×C₅×C₇×C₁₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂²
LCS	G ▷ C₃×C₅×C₇×C₁₃
UCS	C₁ ◁ C₇

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

normal subgroups only

This group has 208 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) = 2730

2856 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1143);