C₅×#73037 #14510761

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

Aliases

direct product

C₅×#73037

Subgroups

	subgroup	G/H
center	C₂×C₅	#5402
commutator, cosocle	C₈×A₄	C₂²×C₅
Frattini	C₈	C₂×C₅×S₄
Fitting	C₂²×C₅×C₁₆	D₃
socle	C₂³×C₅	D₂₄
prime radical	C₂×C₅×A₄	D₈
hypercenter	C₅×C₁₆	S₄
hypocenter	A₄	C₅×Q₃₂
LCS	G ▷ C₈×A₄ ▷ C₄×A₄ ▷ C₂×A₄ ▷ A₄
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆

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

normal subgroups only

This group has 176 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.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3,4,5)(6,7,9)(10,12,21,37,14,23,27,29,15,24,32,41,26,38,13,22)(11,16,25,35,18,30,33,36,19,31,40,39,28,34,17,20);(7,8)(10,11,15,19)(12,20,24,36)(13,25,27,40)(14,28,26,18)(16,29,31,22)(17,32,33,21)(23,39,38,35)(30,37,34,41)

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236459);