C₇×#6891 #13133402

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

Aliases

	subgroup	G/H
center, socle	C₃²×C₇	C₃³
commutator, Frattini, cosocle	C₃²	C₃³×C₇
prime radical	C₃⁴×C₇	C₃
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₇ ◁ G

252 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 189

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

(1,2,3,4,5,6,7)(8,9,11,10,13,15,14,12,16)(17,18,20)(19,22,24)(21,25,23);(9,12,13)(11,15,16);(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, 38);