C₇×#18621 #13195837

order	1792
nilpotency class	3
isoclinism	isoclinic class of #18618
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3498	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

1314 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 4 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 11609);