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C5×#4449 #11746148

order960
isoclinismisoclinic class of D96
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#4449

Splittings

FittingC3×C5×C32 ⋊ C2
HallC3×C5 ⋊ SD64
SylowC3 ⋊ C5×SD64

Subgroups

subgroupG/H
centerC2×C5D48
commutator, cosocleC3×C16C22×C5
FrattiniC16C2×C5×D3
FittingC3×C5×C32C2
socleC2×C3×C5D16
prime radicalC5×D48C2
hypercenterC5×C32D3
hypocenterC3C5×SD64
LCSG ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×C16 ◁ C5×C32

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

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×SD64, C2×C5×#4449, D5×#4449, …
maximal normal subgroup ofC5×D3×SD64, C2×C5×#4449, D5×#4449, …
maximal quotient ofC5×#67596, C5×#67597, C5×#67592, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 343);