C₃⋊(C₇⋊#13049935) #41032006

order	27300
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₃⋊(C₇⋊#13049935)
unambiguous semidirect product	C₇⋊(C₃⋊#13049935)

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₇×C₁₃	C₄
prime radical, cosocle	C₃×C₅×C₇×D₆₅	C₂
LCS	G ▷ C₃×C₅²×C₇×C₁₃
UCS	C₁

104 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.

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

μ_t(G) = 5460

Polycyclic presentation:

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

1788 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 896);