C₅×#5021 #11750520

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

Aliases

direct product

C₅×#5021

Splittings

Hall	C₃×C₅ ⋊ #477
Sylow	C₃ ⋊ C₅×#477

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂³×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×Q₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×D₄
hypercenter	C₄×C₅×Q₈	D₃
hypocenter	C₃	C₅×#477
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×Q₈

192 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 960

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

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

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#71944, C₅×#68260, #14289400, …
maximal normal subgroup of	C₅×#71944, C₅×#68260, #14289400, …
maximal quotient of	C₅×#71626, C₅×#71628, C₅×#69461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4715);