C₅×#4985 #11750484

order	960
isoclinism	isoclinic class of #4656
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#4985

Splittings

Hall	C₃×C₅ ⋊ #400
Sylow	C₃ ⋊ C₅×#400

Subgroups

	subgroup	G/H
center	C₂³×C₅	C₂²×D₃
commutator, cosocle	C₂³×C₃	C₂³×C₅
Frattini	C₂³	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃×C₅	C₂³
hypercenter	C₂×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#400
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×C₄⋊C₄

268 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 960

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

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#71170, C₅×#71178, #14288622, …
maximal normal subgroup of	C₅×#71170, C₅×#71178, #14288622, …
maximal quotient of	C₅×#71566, C₅×#69414, C₅×#71567, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4679);