C₂×C₃×C₅×#494 #14276179

order	1920
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃×C₅ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₂×C₃×C₅×#494

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

1104 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 4 generators on 30 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 1877);