C₃⋊#10620193 #14519497

order	1944
isoclinism	isoclinic class of C₃⋊#10620193
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₃²

Aliases

C₃⁵ ⋊ C₈

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃⁵	C₈
prime radical	C₃×C₃⋊(C₃⋊(C₃⋊D₃))	C₄
cosocle	C₃×#66472	C₂
LCS	G ▷ C₃⁵
UCS	C₁

536 conjugacy classes of subgroups.

μ_t(G) = 24

Polycyclic presentation:

2^3,3^5|a^2=b,b^2=c,d^a=de,e^a=d,f^a=g,g^a=fg^2,h^a=h^2,d^b=d^2e,e^b=de,f^b=fg^2,g^b=f^2g^2,d^c=d^2,e^c=e^2,f^c=f^2,g^c=g^2

maximal subgroup of	#72214225, #72214799, #72224521, …
maximal normal subgroup of	#72214225, #72214799, #72224521, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3891);