C₅×#4752 #11750251

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

Aliases

direct product

C₅×#4752

Splittings

Fitting	C₃×C₅×#101 ⋊ 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×#101	C₂
socle	C₂×C₃×C₅	#120
prime radical	C₅×#1007	C₂
hypercenter	C₅×#101	D₃
hypocenter	C₃	C₅×#456
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#101

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)(9,12,13,22,14,23,24,15)(10,16,17,21,18,11,19,20);(9,11,14,16)(10,15,18,22)(12,17,23,19)(13,21,24,20);(7,8)(9,10)(11,15)(12,21)(13,19)(14,18)(16,22)(17,24)(20,23)

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#69167, C₅×#69162, #14316959, …
maximal normal subgroup of	C₅×#69167, C₅×#69162, #14316959, …
maximal quotient of	C₅×#68132, C₅×#68133, C₅×#68139, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4446);