C₅×#5191 #11750690

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₅×#5191

Splittings

Fitting	C₂×C₃×C₅×Q₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ #495
Sylow	C₃ ⋊ C₅×#495

Subgroups

	subgroup	G/H
center	C₂²×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×D₂₄	C₂
hypercenter	C₂×C₅×Q₁₆	D₃
hypocenter	C₃	C₅×#495
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×Q₁₆

260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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)(10,12)(13,15,17,24)(14,20,21,28)(16,25,19,23)(18,22,26,27);(13,14,19,26,17,21,16,18)(15,22,25,28,24,27,23,20);(7,8)(9,10)(11,12)(14,18)(16,19)(20,22)(21,26)(23,25)(27,28)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#71477, C₅×#69235, #14317221, …
maximal normal subgroup of	C₅×#71477, C₅×#69235, #14317221, …
maximal quotient of	C₅×#71359, C₅×#71296, C₅×#71213, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4885);