C₃×D₇×D₂₅₅ #36339473

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

Aliases

C₃×D₇×D₂₅₅

	subgroup	G/H
center, hypercenter	C₃	D₇×D₂₅₅
commutator, cosocle, hypocenter	C₃×C₅×C₇×C₁₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂²
LCS	G ▷ C₃×C₅×C₇×C₁₇
UCS	C₁ ◁ C₃

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

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

μ_t(G) = 3570

1935 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 305);