C₃⋊(C₇⋊#13049931) #41032071

order	27300
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₅

Aliases

unambiguous semidirect product	C₃⋊(C₇⋊#13049931)
unambiguous semidirect product	C₇⋊(C₃⋊#13049931)

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

128 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 37 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:

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

1725 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 961);