C₂×C₃×C₁₃×Q₁₆ #11929036

order	1248
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

C₂×C₃×C₁₃×Q₁₆

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₁₃	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃×C₁₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₁₃ ◁ C₂×C₃×C₄×C₁₃ ◁ G

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1248

A minimal faithful permutation representation — 3 generators on 34 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1148);