C₅×#67567 #14278603

order	1920
isoclinism	isoclinic class of #4487
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×#67567

Splittings

Hall	C₃×C₅ ⋊ #1369
Sylow	C₃ ⋊ C₅×#1369

Subgroups

	subgroup	G/H
center	C₄×C₅	#808
commutator	C₃×C₈	C₂×C₅×C₈
Frattini	C₄×C₈	C₂×C₅×D₃
Fitting	C₃×C₅×#364	C₂
socle	C₂×C₃×C₅	#334
prime radical	C₂²×C₃×C₅	#108
cosocle	C₃×C₄×C₈	C₂²×C₅
hypercenter	C₅×#364	D₃
hypocenter	C₃	C₅×#1369
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₄×C₅×C₈ ◁ C₅×#364

120 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4301);