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C3×#65044 #11749652

order960
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#65044

Splittings

FittingC3×C5×#101 ⋊ C2
HallC3×C5 ⋊ #473
SylowC5 ⋊ C3×#473

Subgroups

subgroupG/H
centerC2×C3#4030
commutator, cosocleC2×C4×C5C23×C3
FrattiniC2×C4C22×C3×D5
FittingC3×C5×#101C2
socleC2×C3×C5#121
prime radicalC3×#709C22
hypercenterC3×#101D5
hypocenterC5C3×#473
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#101

200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3)(4,5,7,8,6)(9,12,14,25)(10,16,18,31)(11,19,21,23)(13,26,27,24)(15,28,30,39)(17,32,33,22)(20,36,37,35)(29,34,40,38);(9,11,13,20,14,21,27,37)(10,15,17,29,18,30,33,40)(12,23,24,36,25,19,26,35)(16,28,22,38,31,39,32,34);(5,6)(7,8)(9,10)(11,15)(12,22)(13,17)(14,18)(16,26)(19,34)(20,29)(21,30)(23,38)(24,31)(25,32)(27,33)(28,35)(36,39)(37,40)

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#473, C2×C3×#65044, #14429479, …
maximal normal subgroup ofC3×D5×#473, C2×C3×#65044, #14429479, …
maximal quotient ofC3×#10599234, C3×#10599258, C3×#10599236, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3847);