C₅×#85547 #14511285

order	1920
isoclinism	isoclinic class of #85547
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₂³

Aliases

Fitting	C₂²×C₄²×C₅ ⋊ D₃
derived	C₂²⋊(C₄²⋊C₃) ⋊ C₂×C₅

	subgroup	G/H
center, hypercenter	C₅	#85547
commutator, cosocle, hypocenter	C₂²⋊(C₄²⋊C₃)	C₂×C₅
Frattini	C₂²	C₅×#1020
Fitting	C₂²×C₄²×C₅	D₃
socle	C₂⁴×C₅	S₄
LCS	G ▷ C₂²⋊(C₄²⋊C₃)
UCS	C₁ ◁ C₅

320 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236983);