C₃⋊(C₇⋊#261) #11764005

order	1092
isoclinism	isoclinic class of C₃⋊(C₇⋊#261)
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₃⋊(C₇⋊#261)
unambiguous semidirect product	C₇⋊(C₃⋊#261)

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₇×C₁₃	C₄
prime radical, cosocle	C₃×C₇×D₁₃	C₂
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 273

Polycyclic presentation:

2^2,3,7,13|a^2=b,c^a=c^2,d^a=d^6,e^a=e^8,e^b=e^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1092, 53);