D₁₅⋊D₂₇₃ #30655744

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

Aliases

D₁₅⋊D₂₇₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₇×C₁₃	C₂²
LCS	G ▷ C₃²×C₅×C₇×C₁₃
UCS	C₁

176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

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

μ_t(G) = 2730

Polycyclic presentation:

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

1236 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 794);