D₈₅⋊(C₃⋊D₂₁) #36339559

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

Aliases

D₈₅⋊(C₃⋊D₂₁)

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

240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

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

μ_t(G) = 5355

Polycyclic presentation:

2^2,3^2,5,7,17|e^a=e^4,g^a=g^16,c^b=c^2,d^b=d^2,e^b=e^4,f^b=f^6

1404 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 391);