D₃²⋊D₇ #92742

order	504
isoclinism	isoclinic class of D₃²⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₃²⋊D₇

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₇×C₃⋊D₃	C₂²
Fitting, socle, hypocenter	C₃²×C₇	D₄
LCS	G ▷ C₇×C₃⋊D₃ ▷ C₃²×C₇
UCS	C₁

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 42

A minimal faithful permutation representation — 2 generators on 13 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 168);