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C3×#64877 #11746654

order960
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C1

Aliases

direct productC3×#64877

Splittings

HallC3×C5 ⋊ M64
SylowC5 ⋊ C3×M64

Subgroups

subgroupG/H
centerC3×C8C2×AGL(1,𝔽5)
commutatorC2×C5C2×C3×C16
FrattiniC8C2×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C4
socleC2×C3×C5C2×C16
prime radicalC22×C3×C5C16
cosocle#672C22×C3
hypercenterC2×C3×C8AGL(1,𝔽5)
hypocenterC5C3×M64
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C2×C3×C8

64 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)(10,15)(16,25)(17,26)(18,27)(28,35)(29,36)(30,37)(38,40);(5,6,7,8)(9,10,11,16,12,17,19,28,13,18,20,29,22,30,31,38,14,15,21,25,23,26,32,35,24,27,33,36,34,37,39,40)

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10598537, C3×#10598656, #14279239, …
maximal normal subgroup ofC3×#10598537, C3×#10598656, #14279239, …
maximal quotient ofC3×#10598535, C3×C22⋊#3928, C3×C4⋊#3928, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 849);