C₅×#23948 #11946668

order	1280
nilpotency class	3
isoclinism	isoclinic class of #23906
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

1474 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 4 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 16936);