C₇×#6894 #13133405

order	1701
nilpotency class	2
isoclinism	isoclinic class of C₃²⋊H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃³×C₇ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, socle	C₃²×C₇	C₃³
commutator, Frattini, cosocle	C₃²	C₃³×C₇
prime radical	C₃³×C₇	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₇ ◁ G

124 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 567

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2,3,4,5,6,7)(9,11,14)(12,16,15)(17,18,20,19,22,24,23,21,25);(8,9,12,10,11,15,13,14,16);(18,21,22)(20,24,25)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1701, 41);