C₅×#67599 #14279698

order	1920
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×#67599

Splittings

Hall	C₃×C₅ ⋊ #1422
Sylow	C₃ ⋊ C₅×#1422

Subgroups

	subgroup	G/H
center	C₅×C₁₆	#67
commutator	C₃×C₄	C₂×C₅×C₁₆
Frattini	C₂×C₁₆	C₂×C₅×D₃
Fitting	C₃×C₅×M₆₄	C₂
socle	C₂×C₃×C₅	C₄⋊C₁₆
prime radical	C₂²×C₃×C₅	M₃₂
cosocle	C₂×C₃×C₁₆	C₂²×C₅
hypercenter	C₅×M₆₄	D₃
hypocenter	C₃	C₅×#1422
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₁₆ ◁ C₂×C₅×C₁₆ ◁ C₅×M₆₄

116 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 70 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)(9,11,12,23,16,25,15,14)(10,17,18,22,21,20,26,34)(13,24,27,31,30,38,29,28)(19,32,33,37,36,35,39,40);(6,7,8)(9,10,13,19,14,20,28,35,15,18,29,33,25,34,38,40,16,21,30,36,23,17,31,32,12,26,27,39,11,22,24,37)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5396);