C₅×#73203 #14510927

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

Fitting, Hall	C₅×#2811 ⋊ C₃
Sylow	#2811 ⋊ C₃×C₅

	subgroup	G/H
center, hypercenter	C₂×C₅	#5450
commutator, cosocle, hypocenter	C₂²×Q₈	C₂²×C₃×C₅
Frattini	C₂³	C₂²×C₅×A₄
Fitting	C₅×#2811	C₃
socle	C₂³×C₅	C₂²×A₄
prime radical	C₅×C₂²⋊SL(2,𝔽₃)	C₂²
LCS	G ▷ C₂²×Q₈
UCS	C₁ ◁ C₂×C₅

204 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 36 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) = 120

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236625);