C₃⋊(C₇⋊D₇) #64433

order	294
isoclinism	isoclinic class of C₃⋊(C₇⋊D₇)
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₇

Aliases

unambiguous semidirect product	C₃⋊(C₇⋊D₇)
unambiguous semidirect product	C₇⋊D₂₁

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²	C₂
LCS	G ▷ C₃×C₇²
UCS	C₁

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 147

A minimal faithful permutation representation — 3 generators on 17 points:

(2,3)(5,6)(7,8)(9,10)(12,13)(14,15)(16,17);(1,2,3)(11,12,14,16,17,15,13);(4,5,7,9,10,8,6)

Polycyclic presentation:

2,3,7^2|b^a=b^2,c^a=c^6,d^a=d^6

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(294, 22);