C₇×C₁₃×#41 #13089915

order	1456
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

C₇×C₁₃×#41

	subgroup	G/H
center	C₄×C₇×C₁₃	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₇×C₁₃
socle	C₂×C₇×C₁₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇×C₁₃ ◁ G

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 728

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1456, 169);