D₆₅⋊D₆₃ #30655154

order	16380
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₆₅⋊D₆₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₇×C₉×C₁₃	C₂²
Frattini	C₃	D₆₅⋊D₂₁
socle	C₃×C₅×C₇×C₁₃	C₂×D₃
LCS	G ▷ C₅×C₇×C₉×C₁₃
UCS	C₁

120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.

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

μ_t(G) = 4095

Polycyclic presentation:

2^2,3,5,7,13,3|c^3=g^2,d^a=d^4,f^a=f^12,c^b=c^2g,d^b=d^4,e^b=e^6,g^b=g^2

1086 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 204);