C₅×#5233 #11750732

order	960
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#5233

Splittings

Hall	C₃×C₅ ⋊ #416
Sylow	C₃ ⋊ C₅×#416

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅	#67
commutator	C₃×C₄	C₂²×C₄×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂×D₄
cosocle	C₂×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#41	D₃
hypocenter	C₃	C₅×#416
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#41

316 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 28
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#72008, C₅×#70369, #14295955, …
maximal normal subgroup of	C₅×#72008, C₅×#70369, #14295955, …
maximal quotient of	C₅×#71638, C₅×#71750, C₅×#71640, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4927);