Finite Group Databasebeta

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C3×#64852 #11746629

order960
isoclinismisoclinic class of #64849
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#64852

Splittings

HallC3×C5 ⋊ #368
SylowC5 ⋊ C3×#368

Subgroups

subgroupG/H
centerC2×C3#3994
commutatorC5×C8C2×C3×C4
FrattiniC8C2×C3×AGL(1,𝔽5)
FittingC3×C5×C16C4
socleC2×C3×C5#107
prime radicalC2×C3×D5Q16
cosocleC8×D5C22×C3
hypercenterC3×C16AGL(1,𝔽5)
hypocenterC5C3×#368
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×C16

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10598681, #14279662, C3×#10598685, …
maximal normal subgroup ofC3×#10598681, #14279662, C3×#10598685, …
maximal quotient ofC3×#10598645, C3×#10598646, C3×#10598667, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 824);