C₅×#4497 #11746196

order	960
isoclinism	isoclinic class of #826
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#4497

Splittings

Fitting	C₃×C₅×#108 ⋊ C₂
Hall	C₃×C₅ ⋊ #359
Sylow	C₃ ⋊ C₅×#359

Subgroups

	subgroup	G/H
center	C₄×C₅	#213
commutator	C₃×C₈	C₂×C₄×C₅
Frattini	C₂×C₈	C₂×C₅×D₃
Fitting	C₃×C₅×#108	C₂
socle	C₂×C₃×C₅	#102
prime radical	C₅×#904	C₂
cosocle	C₂×C₃×C₈	C₂²×C₅
hypercenter	C₅×#108	D₃
hypocenter	C₃	C₅×#359
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₅×#108

112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 50 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)(6,7,8)(9,11,12,21,15,23,14,30)(10,16,17,31,19,33,29,32)(13,26,24,38,28,40,27,22)(18,34,25,20,35,36,39,37);(7,8)(9,10)(11,20)(12,17)(13,25)(14,29)(15,19)(16,22)(18,27)(21,36)(23,37)(24,35)(26,31)(28,39)(30,34)(32,40)(33,38)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#359, C₂×C₅×#4497, D₅×#4497, …
maximal normal subgroup of	C₅×D₃×#359, C₂×C₅×#4497, D₅×#4497, …
maximal quotient of	C₅×#67471, C₅×#67472, C₅×#67487, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 391);