C₅×#72998 #14510722

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, hypercenter	C₂×C₅	#1020⋊C₂
commutator, cosocle, hypocenter	C₂²⋊SL(2,𝔽₃)	C₂²×C₅
Frattini	C₂³	C₂×C₅×S₄
Fitting	C₅×#393	D₃
socle	C₂³×C₅	C₂×S₄
prime radical	C₅×#393⋊C₃	C₂
LCS	G ▷ C₂²⋊SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₅

248 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.

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

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236420);