C₃×C₁₃×C₄⋊Q₈ #11929030

order	1248
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₃×C₁₃×C₄⋊Q₈
unambiguous semidirect product	C₄⋊(C₃×Q₈×C₁₃)

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

136 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1248

A minimal faithful permutation representation — 3 generators on 28 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1142);