C₇×Q₈×C₂₃ #13046247

order	1288
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

C₇×Q₈×C₂₃

	subgroup	G/H
center, socle, prime radical	C₂×C₇×C₂₃	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₇×C₂₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇×C₂₃ ◁ G

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 1288

A minimal faithful permutation representation — 2 generators on 38 points:

(1,2,3,4,5,6,7)(8,9,10,11)(12,15,14,13)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38);(8,12,10,14)(9,13,11,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1288, 29);