C₅×#4826 #11750325

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#4826

Splittings

Fitting	C₃×C₅×#104 ⋊ C₂
Hall	C₃×C₅ ⋊ #456
Sylow	C₃ ⋊ C₅×#456

Subgroups

	subgroup	G/H
center	C₂×C₅	#882
commutator, cosocle	C₂×C₃×C₄	C₂³×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#104	C₂
socle	C₂×C₃×C₅	#120
prime radical	C₅×#1010	C₂
hypercenter	C₅×#104	D₃
hypocenter	C₃	C₅×#456
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#104

284 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#456, C₂×C₅×#4826, D₅×#4826, …
maximal normal subgroup of	C₅×D₃×#456, C₂×C₅×#4826, D₅×#4826, …
maximal quotient of	C₅×#68294, C₅×#68326, C₅×#68295, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4520);